AL003.300_Conj_sol.ipynb

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    "## Conjunto solución\n",
    "* Un vector $\\vec{x}$ que cumple la ecuación $A \\vec{x} = \\vec{b}$ se llama __solución particular__ del sistema lineal $[A:\\vec{b}]$. \n",
    "\n",
    "* El conjunto de todas las soluciones particulares se llama __conjunto solución__. \n",
    "\n",
    "* Una solución particular escrita en forma genérica se llama __solución general__.\n",
    "\n",
    "\n",
    "Ejemplo:\n",
    "\\begin{align}\n",
    "    \\begin{aligned}\n",
    "        1 x_0 + 0 x_1 + 2 x_2 + 0 x_3 &= 6\\\\\n",
    "        0 x_0 + 1 x_1 + 4 x_2 + 0 x_3 &= 5 \\\\\n",
    "        0 x_0 + 0 x_1 + 0 x_2 + 1 x_3 &= 3\\\\\n",
    "        0 x_0 + 0 x_1 + 0 x_2 + 0 x_3 &= 0\\\\\n",
    "        0 x_0 + 0 x_1 + 0 x_2 + 0 x_3 &= 0\n",
    "    \\end{aligned} \\ \\ \\\n",
    "    \\begin{bmatrix}\n",
    "        1 & 0 & 2 & 0 & : & 6\\\\\n",
    "        0 & 1 & 4 & 0 & : & 5\\\\\n",
    "        0 & 0 & 0 & 1 & : & 3\\\\\n",
    "        0 & 0 & 0 & 0 & : & 0\\\\\n",
    "        0 & 0 & 0 & 0 & : & 0\n",
    "    \\end{bmatrix}\n",
    "\\end{align}\n",
    "Variables libres: $x_2=t$\n",
    "\n",
    "Variables delanteras:\n",
    "\\begin{align*}\n",
    " x_3 &= 3\\\\\n",
    " x_1 &= 5 - 4 t \\\\\n",
    " x_0 &= 6 - 2 t\n",
    "\\end{align*}\n",
    "\n",
    "Solución general:\n",
    "$$ \\begin{bmatrix}x_0\\\\ x_1\\\\ x_2\\\\ x_3\\end{bmatrix}=\\begin{bmatrix}6-2t\\\\5-4t\\\\t\\\\3\\end{bmatrix}    $$\n",
    "\n",
    "Conjunto solución:\n",
    "$$ \\left\\{ \\begin{bmatrix}6-2t\\\\5-4t\\\\t\\\\3\\end{bmatrix} \\mid  t \\in \\mathbb{R} \\right\\}  $$\n",
    "\n",
    "Soluciones particulares:\n",
    "\\begin{align*}\n",
    "\t\\text{Para }t=0,& \\begin{bmatrix}6\\\\5\\\\0\\\\3\\end{bmatrix}\\\\\n",
    "\t\\text{para }t=1,& \\begin{bmatrix}4\\\\1\\\\1\\\\3\\end{bmatrix}\\\\\n",
    "\t\\text{para }t=-3,& \\begin{bmatrix}12\\\\17\\\\-3\\\\3\\end{bmatrix}\n",
    "\\end{align*}"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Representación gráfica de una ecuación lineal de 2 variables\n",
    "Una ecuación lineal de $n$ variables corta el espacio $\\mathbb{R}^n$ en dos. En particular una ecuación lineal de dos variables $ a x + b y = c $ representa una recta en el plano, siempre y cuando $a$ y $b$ no sean ambos cero. Para encontrar la recta obtenemos el conjunto solución del sistema de una ecuación dos variables.\n",
    "\n",
    "\n",
    "Ejemplo: \n",
    "la ecuación\n",
    "$$1x +  2 y=4$$\n",
    "se puede escribir como una matriz extendida\n",
    "$$\\begin{bmatrix}1 & 2&:&4\\end{bmatrix}$$\n",
    "Este sistema de una ecuación dos incógnitas está en forma escalón. Como $y$ es la variable libre entonces le asignamos un parámetro.\n",
    "$$ y = t $$\n",
    "Ahora despejamos la variable delantera $x$\n",
    "$$ x = 4 - 2 t $$\n",
    "El conjunto solución es\n",
    "$$\\left\\{\\begin{bmatrix}4-2t\\\\t\\end{bmatrix} \\mid t \\in \\mathbb{R}\\right\\}$$\n",
    "$$\\left\\{\\begin{bmatrix}4\\\\0\\end{bmatrix}+t\\begin{bmatrix}-2\\\\1\\end{bmatrix} \\mid t \\in \\mathbb{R} \\right\\}$$\n",
    "\n",
    "La solución general es\n",
    "\n",
    "$$\\begin{bmatrix}x\\\\y\\end{bmatrix}\n",
    "= \\begin{bmatrix}4\\\\0\\end{bmatrix}\n",
    "+t\\begin{bmatrix}-2\\\\1\\end{bmatrix}$$\n",
    "\n",
    "Algunas soluciones particulares son:\n",
    "\n",
    "\\begin{align*}\n",
    "&\\text{si } t=0,  &&\\begin{bmatrix}x\\\\y\\end{bmatrix} =\\begin{bmatrix}4\\\\0\\end{bmatrix}, \\\\\n",
    "&\\text{si } t=1, &&\\begin{bmatrix}x\\\\y\\end{bmatrix}=\\begin{bmatrix}4\\\\0\\end{bmatrix}+\\begin{bmatrix}-2\\\\1\\end{bmatrix} =\\begin{bmatrix}2\\\\1\\end{bmatrix},  \\\\\n",
    "&\\text{si } t=3, &&\\begin{bmatrix}x\\\\y\\end{bmatrix}=\\begin{bmatrix}4\\\\0\\end{bmatrix}+3\\begin{bmatrix}-2\\\\1\\end{bmatrix} =\\begin{bmatrix}-2\\\\3\\end{bmatrix}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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+t6ypWLEi3t7eAERHR5OTk8OpU7/+oZbDhg0jOTmZ5ORkqlWrVrzBpdTyr+TJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x650d690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x6432ef0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import *\n",
    "from sympy.plotting import plot_parametric as plt_par\n",
    "t = symbols('t')\n",
    "x=4-2*t\n",
    "y=t\n",
    "plt_par(x,y,(t,0,3))\n",
    "#plt_par(4-2*t,t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Representación gráfica de dos ecuaciones lineales de 2 variables\n",
    "\n",
    "El sistema de 2 ecuaciones 2 variables\n",
    "\\begin{align}\n",
    "1x +  2 y&=4\\\\\n",
    "0x +  1 y&=3\\\\\n",
    "\\end{align}\n",
    "se puede graficar como  una recta por cada ecuación "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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etGvhway1Bxgy7xd+OaTfMazialKghbBhbX0a8+n4bnwyzoDJrDL20zQmLU0n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\naVTdKOcfa14BqoFllsx2udr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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa14c1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7f32510>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Para varias graficas se despeja $y$\n",
    "from sympy.plotting import plot\n",
    "x = symbols('x')\n",
    "y1=2-x/2\n",
    "y2=3\n",
    "plot(y1,y2,(x,-4,4))\n",
    "#plt_par(4-2*t,t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Este sistema de dos ecuaciones dos incógnitas \n",
    "\\begin{bmatrix}1 & 2&:&4\\\\0 & 1&:&3\\end{bmatrix}\n",
    "está en forma escalón y no tiene variables libres.\n",
    "Como la segunda ecuación ya está despejada se tiene\n",
    "$$ y = 3 $$\n",
    "Ahora despejamos la variable delantera $x$ de la primera ecuación\n",
    "$$ x = 4 - 2 (3) = -2 $$\n",
    "El conjunto solución es un sólo elemento\n",
    "$$\\left\\{\\begin{bmatrix}-2\\\\3\\end{bmatrix} \\right\\}$$\n",
    "\n",
    "\n",
    "La solución general es\n",
    "\n",
    "$$\\begin{bmatrix}x\\\\y\\end{bmatrix}\n",
    "= \\begin{bmatrix}-2\\\\3\\end{bmatrix}$$\n",
    "\n",
    "La única solución particular:\n",
    "\n",
    "$$\\begin{bmatrix}x\\\\y\\end{bmatrix}\n",
    "= \\begin{bmatrix}-2\\\\3\\end{bmatrix}$$\n",
    "\n",
    "La solución corresponde a la intersección de las rectas."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Representación gráfica de una ecuación lineal de 3 variables\n",
    "\n",
    "\n",
    "Ejemplo: \n",
    "la ecuación\n",
    "$$1x +  2 y - 1z=4$$\n",
    "se puede escribir como una matriz extendida\n",
    "$$\\begin{bmatrix}1 & 2& -1 &:&4\\end{bmatrix}$$\n",
    "Este sistema de una ecuación tres incógnitas está en forma escalón. Como $y$ y $z$ son variables libres entonces se les asigna un parámetro a cada una.\n",
    "$$ y = t $$\n",
    "$$ z = s $$\n",
    "Ahora despejamos la variable delantera $x$\n",
    "$$ x = 4 - 2 t + s$$\n",
    "El conjunto solución es\n",
    "$$\\left\\{\\begin{bmatrix}4-2t+s\\\\t\\\\s\\end{bmatrix} \\mid t,s \\in \\mathbb{R}\\right\\}$$\n",
    "$$\\left\\{\\begin{bmatrix}4\\\\0\\\\0\\end{bmatrix}+t\\begin{bmatrix}-2\\\\1\\\\0\\end{bmatrix}+s\\begin{bmatrix}1\\\\0\\\\1\\end{bmatrix}\\mid t,s \\in \\mathbb{R} \\right\\}$$\n",
    "\n",
    "La solución general es\n",
    "\n",
    "$$\\begin{bmatrix}x\\\\y\\\\z\\end{bmatrix}\n",
    "= \\begin{bmatrix}4\\\\0\\\\0\\end{bmatrix}\n",
    "+t\\begin{bmatrix}-2\\\\1\\\\0\\end{bmatrix}\n",
    "+s\\begin{bmatrix}1\\\\0\\\\1\\end{bmatrix}$$\n",
    "\n",
    "Algunas soluciones particulares son:\n",
    "\n",
    "\\begin{align*}\n",
    "&\\text{si } t=0, s=0,  &&\\begin{bmatrix}x\\\\y\\\\z\\end{bmatrix} =\\begin{bmatrix}4\\\\0\\\\0\\end{bmatrix}, \\\\\n",
    "&\\text{si } t=1, s=0 &&\\begin{bmatrix}x\\\\y\\\\z\\end{bmatrix}=\\begin{bmatrix}2\\\\1\\\\0\\end{bmatrix},  \\\\\n",
    "&\\text{si } t=0,s=1 &&\\begin{bmatrix}x\\\\y\\\\z\\end{bmatrix}=\\begin{bmatrix}5\\\\0\\\\1\\end{bmatrix}\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib\n",
    "from sympy import *\n",
    "from sympy.plotting import plot3d_parametric_surface as plt3D_par"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using matplotlib backend: nbAgg\n"
     ]
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"432\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s, t = symbols('s t')\n",
    "x=4-2*t-s\n",
    "y=t\n",
    "z=s\n",
    "plt3D_par(x,y,z,(t,-3,3),(s,-3,3))\n",
    "show"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una ecuación lineal en de 3 variables corresponde a un plano.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Representación gráfica de dos ecuaciones lineales de 3 variables\n",
    "\n",
    "\n",
    "Ejemplo: \n",
    "la ecuación\n",
    "\\begin{align}\n",
    "1x +  2 y - 1 z&=4\\\\\n",
    "0x +  1 y + 1 z&=3\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "se puede escribir como una matriz extendida\n",
    "$$\\begin{bmatrix}1 & 2& -1 &:&4\\\\0 & 1& 1 &:&3\\end{bmatrix}$$\n",
    "Este sistema de dos ecuaciones y tres incógnitas está en forma escalón. Como  $z$ es una variable libre entonces se le asigna un parámetro.\n",
    "$$ z = t $$\n",
    "Ahora despejamos las variables delanteras $y$ y $x$\n",
    "\\begin{align}\n",
    "y &= 3 - t\\\\\n",
    "x &= 4 - 2(3-t) + t=-2+3t\n",
    "\\end{align}\n",
    "El conjunto solución es\n",
    "$$\\left\\{\\begin{bmatrix}-2+3t\\\\3-t\\\\t\\end{bmatrix} \\mid t \\in \\mathbb{R}\\right\\}$$\n",
    "$$\\left\\{\\begin{bmatrix}-2\\\\3\\\\0\\end{bmatrix}+t\\begin{bmatrix}3\\\\-1\\\\1\\end{bmatrix}\\mid t \\in \\mathbb{R} \\right\\}$$\n",
    "\n",
    "La solución general es\n",
    "\n",
    "$$\\begin{bmatrix}x\\\\y\\\\z\\end{bmatrix}\n",
    "= \\begin{bmatrix}-2\\\\3\\\\0\\end{bmatrix}\n",
    "+t\\begin{bmatrix}3\\\\-1\\\\1\\end{bmatrix}$$\n",
    "\n",
    "Algunas soluciones particulares son:\n",
    "\n",
    "\\begin{align*}\n",
    "&\\text{si } t=0,   &&\\begin{bmatrix}x\\\\y\\\\z\\end{bmatrix} =\\begin{bmatrix}-2\\\\3\\\\0\\end{bmatrix}, \\\\\n",
    "&\\text{si } t=1,  &&\\begin{bmatrix}x\\\\y\\\\z\\end{bmatrix}=\\begin{bmatrix}1\\\\2\\\\1\\end{bmatrix},  \\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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NjQTNvgy8xr3Uo4EsMOHhjkx3Ei1LwBLf4eZkb7zSmX09nZxd2OmAqgZc5eNhGqfpihrLMwXmkCWJsfP0J5oyhaRZ7YsSg4PN+ouZZKKWRUZhP44NDAODG0n2rclfwOwtiRboV8DsArCyriUTY9weTZPTvghUAFIBF+U+SAoScKmef/99zuqqax8K7QvTtQ45PX3mCvR+GDj6KoBrJhKy96x7fE1SWmlBLdZfjllkOB92IDDABQ2ZuYJTaNXba5XmaVCtMx7hJq6AVivsxt/v5kQ42U1bq70w+XRQGCTDzcsTuOUGymLAkMD4wP3y6WEgtSyK0QrKoDBrUgZE/w+XTVAl2RmKhB32ZoEsJj3yEoOB9w4tKBtaHg4c5WnyfHzNkuuUOWA3MGyKNiY9+31mtCcCYC1kU7R6zhj7zcNLFZSLV5nGlg94bJRET5OA6B8dnm/xximea4hGIME5aJSIFp2hZO9bnr4FAj0yKOoqvd21e5KJVS73wCWJ6UQ0IlK9OtwhVpdVnJ4yG1ZNzlcuQe7XB8qp3B+DMCqfWe9XG0aWC/SG7J7+fDw+xA5yL9Ddnn/dcuY5rkfPxbBGyQCa5mJLJEpGKKlKYCRpIrfDf9ZVy2VytCplHUh+ZzDTRWTqs/inhWAgt+Oawh4KEonCLU58ghJ4YA8t+sWaoOs/UHlQUSWpoF1vaI21ePZmMAwBmYIiAsTEdrQFVdc4Ux+gE9e43q0Kw0d9q/jd5yQtdQ75sYiHj9O8oTX05c6vlOohow88LVg2uyypQJgbUZl+snhoVanvjlltwAc8E9iYuaQo1pdleTwJueTSFtMmUSJDjqRrwFYkyujh74MwOKFF4bLs2HEsC0AdFkARuAHQEj+FKd2TE/URioCQ63/pQCWgtkM3xyn667pigAwgiq6rgzdde6VnxyOjxTtHEuARl4CgqxlrSuXxYKCHJv2zVFOCBO5MtGzzrtM/4j/8rOvNA2sVwk2cL8BWJwQs8LlYcYoq+FF71kAximdEGeNOAS82PjKkoHR5ihgqQBGhCMbVlmidNxb1rsqlbDxVCLuiMiEBqzoMFJP0tXvYu3hMw3ZLvKSw32tjmvK0gmq5HDBRE8wE4A56ES+poFVX4ut3GEAFifWrHD5shIo2jObCECnEYpoLJhT0Fh0Y4kNt6cvtD4FsBQSVdEieZ8nPvGJccJs6apUACyFOVERwz3IgaeuNsXhqKjWXF5yuK/V8W/WPnXJKOvCWAadyNcArKWPuGq3BmDlEiN4Ai0DDckPl8ecx6Zdtjlw8tQoRfoiaIOTKGwb2mLD7SGJxYeAGQjzC859/o1pho1CN4vyt2ruilSYJwAwZILPp8uWCis+MuhHtYLY5HC0UiJmdZ0SsIQ5cVCbmRATmDkDsOJJUHZ5Iu1INsYco9oPQAQrRhmbtl7HfQRhEKgBCPkN0w0BHZgUi9rFF1/sospg+wA4MEVifiQQRElxuT8r96isMGXd5chzSagmoKXLlkJAC+8fwwjSLzn1A8Bi3+XSSy91349aM7bddtuHHOJi+0nlOgOwBGbCACx/ErLY5f3aRT4Bb9FUch0aEkEGhDNnMdMDlDi5i8xw+FZIeD744IO3gGYeC0bIJJGXexSGZPv/j/VvpEJemwqApRIN2S8NLGYbGzYmet7ZACxm5lu+xgAsW8CAF74q1S78siZ6BxoTEW9lNE74h9CI8APkBWnwgWOSzAsKQQMEvGicYskZo/WSROwXplSA84FO/Rs+XZKS3yrQ4cPjuhTK1qMhwwnJyb7LlgqQplRYMzzkDDoTvQFYl1+Y92wDsIdPhIbLA15oT0T4ZVVUJnQcU2BoDgx7xGzIB/ykJz2p0F+WFxTCOOgDqiqYN6BsUvJeQJaNu8z0WHe5KV2SRqf5QMfPNMGWQA7CtX0GCQW5fvnlUgGwVOibUqpLFlaGHnQeRAOwujtKw/cZgD1UoGzYBFSwOWexy/tXEzQAkBSxYBBdCPhA8lvGR5cFYMrUgQkSvkN8TfSlWh/AgSaoJSoaXh5R3aGBEVxCInOWJocsaW375VIBMNYNpuIu2VGQdyq+ScYS0msZgEV9Wo1dZFRSjYky7Y7YgHE2o3Flscv7oyfajE05L3FWNSd46GJMWyGAAaaYHwErLdECNRBBIErei2aH76zLAIpYU5WfTBtqcvzfzw3K0uTQ6Ir8cqloPhwoWD9ZWns/V3+o9fTz2eGzwqKng86DaBpYl6vJTIiZ0tdweYAEHxMaRVE5DBKZMdNk8RcqByKFLNHoaFnBG/5AeC5ApM8k0ZlNyC9gqX433RxTMRM1Fe3ms0iU+eXCABTSHNB8OFB0WcYE9gv8cGWm5ba3gFQ4KnnPYWOiNwBre/VG9m8mxE2CwpcDWPDRY6YjGrCI45B78qoto0mgKbGBsZlC7MpmTN2uoubni0EWDE0U+WN+nhnkvYCXmiNjtZ/I5VD7sqYALGYAWWVMkC/zsXljcX9nEd/2wy+H3xSNuWsC3TqkwjHyr3NNGJk56ES+BmB1VkEL9xiAiTMVEgyBpsTpmQRjAjfKogvzqi3jG0Mz0uKW5GoRLVhGLaT5YtzLJgh4hTlmRLgxLpJ1VcvoJ3jkLcEUxuAz8/tUSWEAStv5cikUGdUDFmu0jJ6shW3lYV2GVRMMwPoh9b89w3xg/ZV3354WhsvvvffeTmOKiS7Mon/iXvK1fPNjLM8hGx/+LcyEjCOLpYCTLACLOdIA7KHLpE5pGfXL+XRJ/r99yqO8MiahX46gHQ4rZRp824scEzdBPpixu25+4dVhYKI3DazrFbX5+eNZA8sLl1eQKIsi0wKThLfTMD8S5k5EoL+pAXT4s2DtKGqYHdEOMD/lPZt+6Ns3R6ag/aQwBqL/CG5ZtGhRo1+X+uVCkNP/+/lyWsJE8wP9fLl+++VYK6zxLomedSJ8UB8GIl8DsEY/sfqdjVcAy2KX10g/ogvZbMqCLvCbYepTehyiAQEzTTLWWQmBLm+2IOpF6yoqhIgznA2VsHrTwB4qybYALObr8v1yHETwUfpRl5ovF5Yw0cTwNngsU2IEIUCJXEVM4gZgMSuq2WvMhNisPDvvzWeXx+fk+wligy6UPYOAj6uuukp23333TMc90Y1sakW5Wpgd8Z3hNysKv+Y6tDSe5QMYDPX9PuH7k5iCBob2i+m3aQ2s6mL1N2v/3rwSJhptyTqhNZUvl0paAe80bEz0poFV/Spaun48amBsFEQcErXms8uriIkAxPkNSJQ1tCY0LkAnjwUdjenKK6/MzdVSmig2X/wmRaZLxkvACUCn0Yn+5lA23rZ+nwqAkXPXdf4VSd2wrsRySYZzkueXU5NlrF8OQE9BHryfvz74HiC2LiPBbmutNtWvcSE2Jcke+hlvAOaHy8PcQKRfuNEAKJjqCKQoa5dcconL+SkDuxiaKKIVGUtRORBCo/mDmVE1rryihWVjb/L3BmB/k2Y/DhRFfjmAjt9juibgB7N0VmI45sx+ae0hgLHOwyKbTa7HfvRlANYPKZc8YzwBWBguj03eZ5dXUcXW5lJ2+MWLF5fWBMuqyhzSRKl/S31xWVNHOD7PhQ9RNTDyx/h/l+XZUwAwojcxH6J1dNmQRdcmXd6fwAmS7NF2srgsMZ2jzbXtl2Odo5UiE9owEPmaCbHLL8x79ngBMD4afEycRgm8yAtTRzR+cEbeNAEkhG3T/BphedeHAJZFExXje9OIRsL0FcDIH8OH5xfI7PfyMgD7m8RTkAWjwWyNph4GFflro1e/nEZZFhV1zWKix3yodfX6vVabep5pYE1Jsod+xgOAabg85UpohKAX+UnKSptgmiFnCxDBzwAYZmly/rTE0ERhQsR8WZS3g3aIc55NSU/OaGSctNE8+mkW8t8vBa0jJQ3swAMP7OGrbObWJk3LvfjlODwS2atBTMNA5GsaWDNrtOdehh3A/HB5Pmj8SzGJnXk+K8wuaDwEUcyZM8dFF5J8rOVN8iYEMx8mS2z/eTRRecwefp/4NxgbzwfE+D/5PgAoG0MYrh3W71Lga9r30Q+/T9lih/iY8PWuOQhT0cD6PSd5fjkOZQRNoXWx7vhuQoq0srlN8femgSUwK8MOYBouzyYP2SsmlTKKKKYlC8AAQzQvogS1aCIaGP/moyxq+CPQ1DjJ5tFExQSPoH1hajzkkEO2mBBDzSM0C4WkuApyyhXog5z+Wzeb2CV62WWXuWKcXZqFDMAeOlupACnfHSZ3Dl2aL0e0bZHZMXbddXmdAViX0t/87GEGMA2XxzTHR4SPCKaGGCd/aPJDXIAHH52vwRHJCGlrWZ9oagRnkGyb53/jlEryKQEZWY13INADANp///23gAW+OMZQNf8JbVIBPnTya04SgJQFcGHiba+h4018CgAYhwktNdNEn3X6SAU4UhnH7bff7tYslgraMJRSMRNinS+jhXuGFcCywuXZ/NEsYkrO4wCHVUNDfeGVAwj32Wefh4QewxjPBl9WrJLNFf8Vvqq8PC9ABI0O31rYADf45DC9YML0AazNQo4KcqEWx//9xFveDblySAjNlk2bK/M+A59vr4VPJbrLVIAjlXEQPMWBR+vmDQORrwFY9OfQ7oXDCGB54fJF9btCKWMqJLcLnxFkvGhfWdGGnC5pZbRTBJDQV552RR+ABXRUMHv4DTBWpnp8bWiHPoB1TRnEuHk/Tti+s99PvM3T5AA7DhVNmJNSALBUytukMg7WsU/xNSxEvgZg7eJSdO/DBmBZ7PLK6h4T5aeCQ2PC5IefCDDLyxlTaqeiWl9cA8hgeixi2WDsBHvgS9LGBw+ocXpVE2EIYCmQtpblooXAFlZk5j2VQinPZFkGcgAYcuqyDhfvqfMT/RG2cGEq4+DVMJ9zwGNehoUH0QCshUVbp8thAjANl8e0RaAE5jo/XF6TgKlwXNbQuAjMAHi4Pi/wo6zWl9JEAT5oGkUsG4wpDB7BPIgJzve7cc1+++23hUEE0yjvrD6Gsndr4/cxOUdlz40N1c4DOGqldV1IEm0ZXswnP/nJZa/b6u8xR3PwosJ3102jdrEeGIB1MxtG5tuN3KOfyoeBH4YPl6AGtC4AzG/4kbDH48cqa1wHOKFZFWlNgCJRgVlFAxkL0Yf40giRR8MqYtkIAYygDcyefm0xvYYNUv1zaHi8W1nBzLJ37uX3bNoAfdvJ1IBcFqsEGh2mXqUoCmt3+aBXpsn1IodUgINvQUv79PI+TdwbMtFzICvLm2ziuW33YVGIbUs4ov9h0cD8cHlOwVmAEsMKryJDo8Bvg+mwqEGsSyBH6NsKaaIAIzaVMi1JNTD6xYxJ0EbIGYe/CbJY3QQg+O268q5/yo5Ydq1colo3hxf1v5F0HgIecwOIhfyAfmmTuukAPI95C/2YrbxwQado/qxLrVXX7+f7z/OT3NVUPOhEvryfAViXq2rzs4cBwNigAAc0JrShUGNRMZcxbOh1BGag1RAaXwY4bJQ4qf3IwSyaKJKX0RDKtCQATCMNKYCZlSCNtsPGpNoO5L68d1EdsbaXGn46apRlVZFu+9navwJYWU4e1/tJt1kRlmrqygM5wC4L5NCEsQAwh102DjRo72VFVPsxxmEk8jUA68fKiXjGoAMYWhW+DzbzPHZ5Xwx5DBt6DR8+/VHFFvNgGct8VuQgQRVsZJjUNIQ81v/G+NC4cHrn5XUBFvStYEHfUPUURThGLIWeLsHfgrk1Jkm8pwcV3FwFwGLGEDJLoF35VZn5Pc0HOf7PgQLg4Od1S6rEjK/omhS0ch2fAVivs9n7/eYD612GjfcAYGGaw9yGSQgtqIyRPYsVXgeGFscmiNkQrS6mpEqo1eXRRDHGW265pfREzMcOcMFakNeI6kLb0Wg7CH7x2WXljzUu9JwOmwaPOuPuAkQBMQ5RqsWhZWMJgGmCn+GzU59PnjbXBshhQWA9x9Cm1ZF17D1ZTPQc0Np459gxNXWdmRCbkmQP/QyyBvbd737XlWl4ylOe4nxCqpF883d3yINj6w4l15kAACAASURBVGSneTNkz61HZMf5M2TihE1nEPxH+CdCR77mWilLRmxJFfpUrU4BEPNRaOPPMjWG0wYYY45kfEXBEBrir+wfKTjs/VDpHpZjT7d2AWDhgLNMdxxyQj8c/1f/HFo8IMeayYqw5GdVN3w0csCzKL2jJ2FH3sy6Z23wfdKGhciXdzEAi1wEbV42yAD285//XI477jg56aST5PDDD98CSid//y9y5a0PishGmT19imw1fbJsO3ua+7PxwXtk8b67yqN3mC/TJk/c8lFhlvPNdlUCPgAwkpzxTeXRRAGQbLB5zn0N2iDZGb8bJ/i8BsgRGanRkSlEvqWQRJyCHw4NXDk3q3y3yhGY5Y9TTY7+tAJBFtABcmqy7jq5Xd89tA4YgFVZFc1daybE5mTZSE988C9+8YudWe6jH/2oM835Ws/qtevlxiWjctPSUfnrfavk5qWr5Np7VsqDK1fJvFnTZavpU2ThrKmy9VbTZOqaB2SXBTPkkMfuJnNnTt0CamFScd7AMUtiHiLHKy/kPitJWfvT3CF8WJycy8iBlX+R69iwOMETNdll7hFaIe9exgnZyOTndJICgOF7wgcWk2tYVRY+yKkG5/vkWEc0vgP+zWGIPEgf7HyQq/r8OteHAUbDwoNoGlid1dDCPYOqgbGJf+ITnxDAAwAj6KJIa1HzxSVX/UUenDAiS9ZMlJuWrJKrb79Plo2ulYWzR2T6lEkye/okWTRrqmw7Z5psWHaHHH7g42WHedMLS69feumljguxLOAjy/8WMm2QQE05kKKSIPi7iE5EYwTAQj9DC8uktEtyjgCvojprpZ30eEEKAOYzr/f4OrVuZz0BXlQowAwNmPlanQ9yeT65JmvKER2LFqbfhgFYrWnt+SbTwHoWYfMd8DFgujvnnHPcxhnDQs7mD9ARKMHpEFPLjns8Wm5cukpuRmO7b5Vcd89KuWf5mExYNybz586WqZMmyNwZU2T7udNkt4UjstuiEdl1wQyZNmWSC7cHdLDxF1W+5e2zACxk2vDHlycxtE42JhK11WTUNXGrz3fX/EzH9UjSOGkKZQeZuN7qXZVCUjkjLzLpKsiFdF7qkyuqKafaXCzIhb64YSHyNQ2s3vfR+F2DqoEhCD5EAib+4z/+w502ixgzVHB8UARwaDHKrIALrl21Zr2cf9FvZNrWOztT5PX3jsqSFWMydfIkmTRxgqzbsFGmT9woMzeOyi7zpskT99heHr/TQpk9Y0ruHIUAxmmdDY+cLgUiBacixnzy1ABfgjfIReIkTfQbvjNAtF+sE/6LkvuETGPmoPFFvLnDFACMyFXMe0SJdtl61Uar1JRjzWVpcxyyOCAqE/0wEfkagHW5ur1ntwFgr3nNa+T88893mxnh1WFjIR9//PHyox/9yAHPueeeW5u5AA0MAAOUymiaGAcmDXK0CHXGb1Z0Wg9LqmzYuFFuWToq1y8Zlb/c+aD8/sY7RKZtJctHV8mkSVNk1TqRWdMmOQ1tl4UznV9t90Ujsu1Wm9jW/RpjGrTB+P0Isxh2e7Q23uOggw5ywMeGqVWawyAAZK1h3ABbCHBsLk1QK6GFEgVaVlamzWUPGwimqi41sFSi/zSgqMwq0Mt85IGc+ufQ5FiPABlrg7XGwazLNdLL+4b3WhRik9Ks2VcbAHbRRRe5TeSoo47KBDCAC/8VfxMGD5jxd5329Kc/XT74wQ+6jTnm1EuUGP4aqKbK/DV+SRV/bCFN1O+uvlbuXTNV7lkzSW5bNiZLVq6R+1aulZVr1smDY+tl3vTJsvvWM2XSqmXy93vvLDvNny4rbr9OHrvPYx7GtIFGRgQkPr2sxoYAsGICBYBjTIiMNy+6jc1GQc7X3HygY+Mpq+nVZk2y2HWRAp0VGjSyCnk4Y9+hqet8/sGm+qzTDwdYgptYQ5goWVddBvrUeYe8ewzAmpRmzb7aADCGgunguc99biaAvfGNb5SnPvWpcuSRR7pRE7F14YUXljK1Z73iy172MnnDG97gknqz+A/9e9io+aDYzP2SJXmi03wrnx4piyYqy+w3uma9XHfPCmd6vOPBMbnj/tXyf7ctkdUbJ8vGdWtlwVbTZccFs1wU5I5zp8vuW4/I7otmytjy+11idhYYA0ScrAFeIg+Rm2pPvfrAlCRX2SZC/wgyyip3okCH5ggAatHCmsuxp9tSALBUwtd//etfu4oFTWjXvUyKT/LsWwN66TOVew3AEpiJLgAMYHvXu94lixcvdhJ4xjOeIaeffnqt0g9vectb3P2c8spY5qF4wlcEEJSR9DKurIjALJoo/B4xTPN//NOf5a6VG+Se1RNlbMpsF+J/w5JRAezmzJjifGuTZL1sNWm9PG7XbR2g7b5wRLaZvUkDQnPE5Aqg4j8j7F41o35sWFqd2Q/hVqAj0oyxhCZK1er4eazjv+5n0S9G/KLxQUPGu5aVzan7jrH39XqgiX1O2XX4fTGTM/cGYGXSau/3FoVYUbZFGliTAHbqqac6cxu+Dz6UvKYUT4AcpkFlBih6Ld7BDw7Jo4mKZZpHQ0DTIZlZgYeP+p4Va+SGe1e6YJH/vf1++euS5TJ52gxh0a0YWy+TJopsNzJRFk5dJ3+3906y3YyNMml0qTz+cY/dcsLGBMs7VWVsqDituZfDfE5ACT4OrQwQAl1RdJsGAvQCcikAWAq+QCYpFQDzmeg55LFGhoGJHhmbBtbU7tFDP11oYE2aEM866yy3YQJeeWZBTHKEFWtpEuikYkyIOOQBGvKtimiiiAjkT1EeGGMAwDBzFkXqEWACcO60+14unB8T5A13PyA33rlU1kwekWWj62TN+nUyc+IG2Wv7BbLdnBmy47zpsv6+2+TZ++8r82eP9LAa6t8a6/sJHf+hyRItj5bHOAHQ5YF0CgCWQjpBagB24IEHujkFwLReW/2Vls6dBmAJzEUXAPbDH/5QPvnJT24J4oAOClNDnfatb33LAQNmxCxQIiCC32Nu09IkRYS+/hiI9AMcAbAimihqLxUR/yrTBn46/hQBWMiZqPeiOU6dPkNuXLJSrrnzAfn9dbfJ2unz5Pp7VwqsIxPXr5GRkRkyMnWKbDd3U/QjfrU9Fs2SRVtNLQ3CqCN7/x7Ang0qL/ikSv9ZeUo+0KHF0kLuQMYACTLh/F1poiQQE2DTZaAC8sOkrMBRRfZNXzusTPSmgTW9Umr21waAEZxBUAah6oTMvu9973PsALQ3velNzhZ+7LHHyn//9387Ex2JyHVLn/Oc8847TwjmoA8/Wk6jBSE09TcUAAywK4usw2QIOStaURFNVFGlZ59pA5MaTvWiQAfkRKAJGqXeC4D6EZN6jb7DXQ+OyU8u/5OsnDxbbn9wvdy7co2Mjq2TsXUb5MFVa2XeyBTZfdEs2XHeDHnkfAiOZ8nOC0ecz62pRhAH4yqrn9bU87K4AzFjckhhHFmlTkL+wLpFK4veIQVOSN6dNb7//vs3Je5a/XDQIBpSxzFMPIgGYLWWRPM3tQFgzY8yv0eYrk855RRH6ks5ET15s8FxGiacPwxpJgzdvzavdzQr+gA8ispSoOURsZgVGOIzbVBgEBNZUYg1HznjA4wJCKCFz2ZjQKuE+1A34bCcyfJVa+Uvdy+XG5aslNuWrZbb718tN967QsbWb3SsItMnT5Q5MybLI5y2NmtzFOSIjEybXGv6UkjgRW6kFmhJnSwWeD+6UkEujwGen1eN4kuhrAzrkaTuGDN5rcmOvGmYmegNwCIXQduXDTqAQZ760pe+1OWCsdFrGRJ8Mvit/KKSKsu8/K5Q1vRB1CGmmCJtDUDBxBhqkSHTBmPNC5H3n82pFU0GUMiqLq01yDjZKoABoGi7RRyKa9atl5scq8hKufHelQ7clq5c6zQ9tLWVY+s30WUtmiU7zJshOy+YKXttgwlyWukyBJwx83VZfwryZUzFZTXh/JeJqczM3OeBXJgI3isDRqmgIy5IobwOw+QAiD9X69QNEw+iAVjEQuzHJYMOYGg0nDQ/97nPbWFxx3QJ8KARZZ2g2ewxyxVVD1btC40urwRKCDr+iTeLaSMm2IM+iShk09Tw46x1oKYZBbC6wQOAF9rZX+5aLjcvXSl3PjDmNLZbl406EyPUWCNTJ8m8mVNk5wWb/Gr413aixtrETeVoaClwANYBsJhvrEoiOOkERGKythT0YhLBY8YRe00KBU4ZKyZ4Dm2UGKIZgMXOYPPXNecsaH5sPfU46ADGBsxG/6UvfcnlRxGlBkBpxGGWcAh1hvg3z9GOrwoTDKd5fBoxphgtasnz/PIoGjiiJ9KyKs9ocxdffPFDCnTGAFjTTBj3j66R610U5Eq54Z4Vcsv9q2R0zQZZtwG/2jpngtxt6xHZfu4MeeS86TJ/8hqZP2lM9n30ps2qiwaAEewCYPS7MW+YzNDu0YR90GM90cJEcD9njoCUMp9s7DtlFdWMvbfJ68JDzTAR+SIni0JscrXU7GvQAYzXBqy++tWvOgnw0fgRh1liwdmvvGzh70OaKB+YikSs1wGogJ9fHFPv0xB5xpfVuBfAfOCBB0ojyEINDFMNm2CbTBhja9c7syPh/bcuWyW3LVvlQG5s3XqZMXkTcC+cM8tparsuggtyRPbYekQWzOoPoJAeATFyFwCm81k0Bk0Ez6L1wm9FQ6POo/SKzZFrsyZZlW0GKwhrWiNTDcCqSK/Za00Da1aejfZ28MEHy5lnnulMFpgrivxAPDiPOSOLJqoKgJFITOAFm1AWFRQncYJC8lhA+ODxX2ACwmxZFEDAuKAK0qCV2DysRgW/2Sx0+wOr5XfX3ylX37pURieOyNLRtbJs5RqXhE0pmm1mT3fFQ3dwlFmzZI9tZskOc6bLJDK0G2wpAJjPPFHn1RTksii98hLBfU2O9aCE1ZSW6bL5VoFhY6I3DazLleU9exg0sBe96EXytKc9zQFDERuHvnZeMEUWTZTPIF80ZQRxYDrC/+aXR/HvYXPCyZ/lU4Piig+e8aPBYQrjxJ3X2KwJGlFWg36HsYfjCv0d960ck2vvXiF/XbpKblw6Kjfdu8IRG0+eOEGWr14nUyZNlN0WzZQd5s10idh7bD3L+daosVa3pUBge9lllzmTcxsh+sjFTwTPAjnWGNoczyfnMEub61eOnJ8Tx7hpVQJs6q6Dft1nJsR+SbrgOcMAYIcccojzf733ve91YdRlDbAgQtAn/82jiYoNuQfA2DiK6Jw0ejD0qanPjWgtPnBAjrEVfeyMC9OpXtN1EEVYOj5rDlavWedK0QBsmB8JHrnh3hWyZv0GmT19iqzfsFFmz5gsuy4YkZ0WzpSd58+QvbbZSuaNTC2bUvf7FADMp06KGnQLF2FOpmGJUFov32yZlwju81Y2AcD4A8nBJKDFAKyFia7QpZkQKwirn5d+5zvfkXe+851y8sknu00/hqQ39EUV0UTFhNxj2oH5APNlWUHH0CQZ+tyQHblthNH7ASChTNHS2BgATTYePXljNuL//Tpl67jqBg6sX79Bbrt/9Sbm/ntWON8aof13PbjaFQ0F2GZPnywLZk2VXamGvXCmIzneft7MhwU9pAJgXTNgxAT0hIngoTbXRCI4h6xHPepRLrBq2Ih8WfemgfVzp8951qBrYJdeeqlQf4z8LzSYGEYPNn3lRmTjL6KJyiqp4otSgzbwV5GgTHRjUQtprAh/B3B8CiZMLwRjFIX5Y0LklAxoosFhukSzBPTYjPwNKI8hvmqSbtF7EXiCCbasIkDskl+yfEyuu3eFy1sD3O58YLWLglwxBhfkBlk0a5pj6d929jQX2k/u2n03XS1P/rsnFZpeY59f97oUSHTrplSE75yVCO4DnQ9KWXlyWBL4HjlMcS3rbViIfA3A6n4hDd836ACGOL72ta+54AhMibBTlDVlu8Dcx0dWRBN13XXXuXD7vMAQQvLV3ALrBzx4sQCG2Q/g8cuicC/PhP0jDwzRGAEwzKWMjeejAeG858RLODZ/8pgo2ITCQpY+yOm/q4R2kzdHdCf+v7Ya9FjX3rNCbl66Sv5636iLgLx3+WqZPGmirBxbJytHV8qjd1jo2EWgzSJYBN8apWr61VIAsH7SWRUlguNr5kAFcBEZinVEiQb6NR9tPsc0sDalG9n3MADYT3/6U/ne974nBHPEABiiQRNi82ejL2KPCEuq+GIFMPjDpg2RLCfNsjpQAA9BHJgxAV2CNkJzH5GMaF9ZFaOV9QNwIcgDRz2bA2YjzId5uW0KaptPju41+JnmLwFo6ifRUzaaKiDI+LIATk2V9NNV8ix+s78u3eRXu/SP18iGmfPl5vtWy9r1G1ygyIrV62TByFTZddGIPGLuNNl1IaA2Io+YM72xvCt/TaQAYCmwgSATlQUgx6ELP7VpYJEbc8OXmQ+shkAh6z3++OPdJvm6173OFbH0G2anV7ziFUIIOKa8E044QY4++ujKT4IXECopiIIBhBgHNKZHPqi8iEEdhF9SxR8YG7YPQDE8h9yvJT/gzMvLV0OTARyIavSbH+aPdsamAMiQFsDveG82CwAFUKMP/Vv/zQaSZTrUJFr/b/03Pj7ALauQpZY/oU9+T/4bz/IBL2Y+Kk96xg1+TbR7MEHevcIFidz+wJhjGYH0eNbUyS4Ze+LECS5PbYd50+WR82fKnotGZOeFM2Xq5PpRkP6m3cT71O0jhbIyISM+65IDV799s3VlGHOfaWAxUmr5mrY0MECLoAq0ox122MGFFsMa70cJfuADH3BJu1RjxtwAbyFmtaqnNDbwo446yrHel0XvIU7MXTiYcbaXPYvxsDETTaUti2kjlueQ0zGyQSZ55kZAM4u1nvfEz0XdMcYNMKABAp6YZxRwisw6eawQPuDlJczmgRyblaYB4AcME3VDUA19ciGfYN0lX1bUc8XqtY5ZBJ/aLfetcoBGeRrZKDJj6iQZW7tBtp0zTXZZOCI7zp0uu5GztvUs2Wp6PMFxChpYCsEsHGxgRiFXkTZsTPSbLRgDo9gMzECrfvxtARhReVRLvuCCC9yQ0JBo7373u7cMkZ/h+KcoJaa6Zz7zmYIDumpwAVoIxLaf/vSnHTCgWeU1DVln80f7KgMwwuvZnDUplA8REOI5vokPHxT+LOpRFTVMl4wPX1Vey9LmVONTqiRABg2MseDLK8oZy3qOmg6zWCG09I1fVDLU5EKtivcHYBlfFtDlgar64xijUi2FAMf/Y1go6uRgYWp0Jsh7NgWMEP1489JRR5cFcK1eu8Gx9mOC3H7OdNl14UzZc5utXABJFvVTCgBWRw5V942y65lXAqA059EArExi7f7eAKyifP/zP//T1fv6/Oc/7+78yle+4khqKWSpjU35iCOOcKY4/v2Nb3xDDj/88IpP2pTcSU7UueeeW8hx6Iess9mWhaqrtubzF2rQRsi0wfjRnIqACTDkXdFCi6IVQ21ONT4iDnGCs5nzzpxw+VlRtGJlYW6+gf7VdKggpyZE/tZcIoCNQwDvRiQlY+FnqlVpMImOo8hUyak9yxfH85WFIixi6ZsrtdJ2ryZL1sk9y9dsDu1fKXc8sFpuu3+Vi4ScOXWSrN8gMmXSBGdyBNR2WjDT1ViD4Pg3V1xeSgNWd05i70shFy2MSh02Il/TwGJXY8vXtaWBxQAY1+CLggaKIAQ0MM1vqvrahNDDh8iGBht42EKaKDQ9crYIgihqaDkEVaBZYK4jAdrXMvReTpyAW14UHr8np4znEWhRVLHXZ61n3NyHuRGNT31YRJoBFmiCXTU2JU1JQEvijw92Gjrts7L7/65jqgTI8kCOTZNIUF9bDLW5qtq9L1tqrF13LwTHMIyMyl0PjLloSKIgJ0wQWbd+g8zcsEoet9v2suOCmbLHIrggZ9WusVZ3XlPQArFGcKjBLUAzAKs7m83cZxpYRTnGmBDRtgjsOOigg1zvT3/60+W0006LjiT0h4Q/C1Mkm1dWwciQJgpQwpRXFvbOBk1iMX6nvKhBxuFXUg5FpZGD+OcwtWUFaPj3sBHje+PjJ6CDDRuNjw0f7QKNkM0hC0grTlPPl2Pu1LFkdZZnquSdlMAWx76fR+T74/Kc/lmaHBo+vlYf5MIEXc1d8lknwmdXYYWnxtrNsIvcQ4215fLnG2+XFRNnyXryniaIM0FuP3e6bLvVNNlh/kwXAbn7wpmyzZwZPcs+r4MUACysDzdsRL6mgbW2fKt13JYGhjmIDftnP/uZi0xjYyFfy2diP+aYY1ykHb4ytBvs5WhgWeHjZW+FKfId73iHzJkzZ4u/Su9Bo8HHhplRT+AAGmBQxt7Oh4dpigZg5OWx+JWU/bGq5ofmxbPyohr9e6glRmQmIfk33XSTMzlq2DymSrSvIsqqMlk19Xv1wWmyap1+fW6/LH+cb6oMoyr5v2qk3MvaIY0iK5LS/1lZfS/eQ1nhs9IHANUskAOU0ZaZG8yN11Bj7b5Vjl3klvtGZeWa9bJhw6bioRQJXTRrqstXIwl7961nyk7zR1wNtl5bCgDmk0sPI5GvAVivq7Sh+9sCMIb3ox/9SN72trc5f8lrXvMaR/dEoAWNkHc0iVe/+tUuio5FjjZGWH2dRv8vfOELnflQC+jRTx5NFBoOGoDPgJH1XDY76nMBvGXAmsVcD2ABOuobi3kuWsM111zjNC/AC9Bko+ZQAJgCpJjKumwK7GiJHBrabH5Ctu+HU8BTQEIm6oPzTZV5Cdll/rgQUFWb09QBNGIf4DgcMd8AWJYf7oFVa+Xau5fLjUtGXRQk5keCRUbXrpMNG8QFi8ydOdX50qiGvQtmyK1nycxp8VGQyAJN9IADDmhzSkr7DpnouWGYiHwNwEqXQH8uaBPA+vMGm55y4oknOv8TScnqhyqiiQqjC/PGil8L0Fm8eHHp64QAhimQ+9H8dEPDN0AYf1HyNBsn0YqAHsEe6itSX1hZsnTpQBu4ALYQxkUgTNcNbRqtlVSHolpbvqkyjKqsYqrUwBQOQOqPA9w4qLCu2KjD1IHQZKlBLmvWbXC5aoAaIf233jfquCCXja6VyRNFpkye5LggCRTZce4Mxwe55zb5NdYYE5poTBHWNueNCER8zPh6h5HI1wCszdVToe9hAbAzzjjDbRxoJ5yANfgBjSyLYBcQKauODHAREcjmxIZQ5hvxAYyNhARrwJRTuraYcHsCTHgu5jA1kWGSgb2jKMqxwrT3dKky95M0XiaTnh4UcTMyAdhjSphkRVUq4KlW5Uc5hiCXFwCiLCcAmNJp8TNNHfBBrijIRSMqee6S1RvllvvXyg33jsrt94/KnQ+ukXuXj7koyNVr18us6ZNl5/kzZTvy1RaOOILjR84fkbGx1Q8JX48QYSuX+Gwgw0jkawDWyrKp3umwANiXv/xl5y8iIITNDBNGEU1UWdSgz7TBx0iUYxmLgNJEMQucgtEIQg7FsnB7gAtg5Tp8h5gPMcFS76tOvlf1FVF8B8BM+D7+yi4rHzNKAIKx4GttwowZMrT72hwgpFpVXlQl649xhBpykanSp/LyA074t+bjqea4ZsIUuWvVRLljxQa5d3SD3PbAGlm2aq1MnDDB+dXIW5s7baLM2DAqBzxmV9ll4aZIyOlT402QTa0X5gWzO7IaRiJfA7CmVkqP/QwLgP34xz92eWfPf/7zXRQi4e5FNFFFxSU170qDNmJKqjANaFz4rDiF55nX/LD8cOrUX8dztTwKGgbaF74dfhZuoiELeBUC3qpLh42Id0S+Zf7Aqn3XuR7AQB79rDwcBoCodsWBAzMm2naZqTJLa/W5KjdvjlsImTU/LgQ4V+trzVq5ffkGWTI2SZasmSR3rVgn942uk3UTpsiUyRNl2pTNfrUFMzdVxHYBIyMyP7LGWp154R4/mRqZIZOqyfZ1n92v+4xKql+SLnjOsAAY2s/HPvYxedWrXuX8TVkkub4Y8opL8rGhPfmbdFlJFe0XfkOABt9XXoi7X8rFH4+G2uMbow/1ewEYIe1UURSdhqZzf14+VN1EX4CZTVNze7pcvpiASWsgArKX3K4m3oG5U/omAAzAyfLF8bPQVBmaKfl/3vzkRVf6miMHt/uWLZOVMkNuWjoqNy8bk3tXrpclq0VG10+QGVMmyZoNIgtnTZXtZk+XRy4Ykb22m+OAbcf5MxozCfuRkAZgTayy3vroPba1t+e3dvewABhaCmH5kAbjO4phpwhrcyHkrOCEspIqOjloamhMRWHlbHaAEuZAvwGS5KWRVqB+LzQMNrwyeqpwceSFpusJng2FllXDSUPVQy0hNcDgwIKJqutoTOSIzxLgyso/zPpwleVEabTKuCN9kNPUgTwtDr8t/XIQ8rU65vyOpcvlL3c+INfdvVxuXTYqt90/JivG1suqteuFDW76lAmyYOZkxwO504IZssfWW8me282VObM2sb9U8XcagLW2Zdfq2ACsltj6dxN8hWhdhOJjRiyqZqyjCgFMgzZC7amopIr2BdCQvI05qyi3jM2L07pf9gWfF8EdAJWS9JK7BoDxTm1oGDGEv5oLxZjI0yOZmnw2NtEuzUFZRUD7t9Ie+iS0bQ44HEiqbPBl442dH8AN8FT6Lny/mLE5DOWBHM/W3xEQAsHxTUtXuYrYdywbdXlra9etkwmy0bGLzJ8uMneKyDYjE2TH2VNkt0UzZdGckYeV2FHNMYuJXtd12XsP0u/NhJjAbA2DBsYHQx7Y//zP/7i6YLBrlFVGRvQ4mjXEPSyP4k9NHju8XqMRjwANEY9ZUY9+fz5w6nOVWBhg4EROSYyuAyXUFEZOmmoBeVF7bTHMh58IQA+LCrJpEjDqfIqADIcRDjwxB6Y6zyi6R+dHc+M4ZOC/ZQ3VIWTWZ23YuFFuXbba0WaRr6bM/avWrJex9etl6sQJMnWSyNYzJ8rC6SKLpm2QRdPWyfxpm4ARsGJdE8SkkZV8k3VN103Lran+DMCakmQP/QwDoKNWMwAAIABJREFUgPEBn3POOXL22Wc70mA2kzIQQWREFxLBBvBg1stj2sgqqeKLHA2NDYNNPKsMSjg9Gm7vk/QyZo1ypNQLJqC8KtA9THflW0kyJ3cty6cXRu2piVIDG0IuxNBkWdUspYnclI7xUxMqv1RDN6DtMN8hsXND3VfqBtkrE4lq7FmEzL65Uk3JvhYXJoD72j/Vr6+7Z5O2dtv9q105GuquTZ08cXMU5BTHLvL4bafLrpM2kTvzPJp+Z5VeKvGLDcASmKBhADAVI2Y52O85ARKCXtbwO3EdG1FRZF1R0jOmPoIb2FRxoMewe6CB4Scj6CMk6cUcBZCltCn2Er5ftWxLCHL+qR0KLaXkKpvbtn9PxCHjSSGIhHfVwKOqhx4lZM4KOuEgUkbIvGbjRLlhCTyQmB43sfbvOX+yHLTtRseIg0YGI8+hhx6ahL+yyXVhANakNGv2NUwA9pznPEdOOukkl4sTAwCwZHByxV9QxCjhk+v6YlaGecyQgGYMywb3Y7pko0ED80l6yQHDXEl/KZjHmsyxylueMVqCBiNwOCAi0zdXtpk2UDRmgkjYoItqz9X8JCvfxrrBSpBXCaFyh8ENZYcQ5pB5UD8cpky+Jw53/O64444Tgjq69Jv2KoOs+w3A2pBqxT77AWDkZx1//PEuIZcoQQItwnbhhRc63kQ2dXKMfvnLX1Z8E3FVmV/2spc5PkRMFmUNDYiTZ5kDPit3S8PeCbzQJFoCSdDCyp6NCZFNGbOckvQChhqdWFZks+y9mvh9Xt2zJvqu2gdzBJhSEQC5q8+HnwNqbJJ+8c1QiytLQK86HkzGmDMZT9dNQ/gJ9ukqsdyPeiXhHu2Ub+K9732vq+SAGZL/811+5zvfKS0i27VMY59vABYrqRavaxvA+MDY0H/605+60zMsGeedd56LlNLGxk85FIAOuzkgEOPDCsXy9re/3fWPVuOz3meJDyczYe+YDsvCn7NytzTs3a/HpSzy/ruFz2bzJclTi1qy6fSTGDdmKWkEZAqBEmyO+Cpht8hbE1UZ7UOAU17CGNlwmFHqqjaiQ2PG4F+DyZn3KVvDVfutcz2gzuEMsyoHiosuusj5pQmsYo2jJcaY9us8u4t7DMC6kHrwzLYBLKYu2Kc+9SlHn/T+97+/J4l88IMfdD4SwIsTaV5TnkI2RQC2jJA2LJXCKROzIryEvqkPjYAQb2inshr9oGVxDyZE/kAVpczdZcz4PQkn8malikJ+KbCHa4pB2YGk7PV8Rvssfw/3a9pAVn6cH2BDqkRZIdSy8TTxe/XDxfB0NvG8sj4AU8y7HOoAs2c84xmuyGyZRaKs31R/bwCWwMy0DWAxlZnVdIi5Ac0IcyPmwKqNAA60t/333z+XjVuZNgALTtD4rWIShTVykIReQIoNPgwLLqKn4l3ULEeIP+HgaGMAIX9n1bryN9J+nPaVKipk/qg6D01dr+kEbNBNmwGzxhiGpftAp9ReHD5gWM8CuX7MkY6buSJalbUbk7Tf1Jzk9aOaqdZj++IXv+jyGD/ykY+0/ejO+jcA60z0f3twCgB27LHHujpXFL/EF0Qtox/+8IeVT27f//73ne+MSs955SR8po0Yk59KSqmCshjm/U2F98h6tpL04vjHx8WGzPPxw2FyAQxDtnQ/LB3gZYPM2jiVf6/XwA/YTHhmClRRukFjDq4aWdfGZ6VgSrRpOE8KdBqxFzJnaC5U1bSBovdAM+Uw5de+a+O9Y/v0oyA5lD3rWc9ydfRS0FRj36HqdQZgVSXWwvVtA1iMCfG0005zG+f73vc+94avfe1rXdjtS1/60kpvzLM+85nPOO0NUAg39JBpA80HPj02pbJG6DsbEJobJ/C8llXU0ifpZXPT4pTK2B1Lh1QWDcaY/HIgfg2qMj8Pmi9+vVTCwgFTgCEF85NqplnVBcJ1oEEmRXXJigJOYpJ9AVAOSuprKlu7bf8enyk12fQ7onAthyCK1g5zMwBLYHbbBjBML2xCaFc4cNFOvva1rz0kyIKNEy3sggsucFFlmCG+/vWvuyi9Kg1fEubHd77znQ8rf5LFtKGRhGwEZe3SSy91UVRlzOchgOkzuI+Qaz2Fo3kBhEW0U2VjCn9fVA6EDdXP6fFD0RkTc0AYdiyYVh1blevhk/Q10yr3tnEtydyYfIuCc2Kf6wec+OzyfnVpDl5ZWpyamZkrzNApFDZVNhL8vqwpzOSvf/3rhe+lH2bfWLm3cZ0BWBtSrdhn2wDGcEhkxM/FZg7lEye0T3/6026kekr78Ic/7Ng0MJMRas/1VRsg9cxnPlPOPPNMBzQESNA0aCOLaSOL0Dd8Ln41/F5E5WmfRRqYr/2x2QAKgJ+S9JLrhfmniQ2xqoyytDg2aDZNPf2rFtcveij/HTQiE9NYCr4dDWrpp7ZTxIOINo/lgDXFWsyqONBP4EDzYjykFADORx55pPt2n/70p1ddmgN3vQFYAlPWDwDr12vyAZEE/IUvfMEBBrknftBGlumvDMDQBggugeoJ82FZ4qrPr5hF0qus7uSexZiL2pYdSaf80dppefRQaAjKzFAUrddrsmpZIdK25RH2ryH8MKZ03RTcicjkkKGUXb65Eq2OQwqtSItrIuBETZkaZEMu5+c+9zmX69WrP7ZrWcc83wAsRkotXzOMAPalL33JgRcJ0VnlUXyRat5K1geH+RNSXcLl0VLor4wkGGc22gMnd/xraH1sJEqwCsBhbinT5Fqedte98udVpYpig8wyf/n1rsLNU7U51UKz3g/nP5ou42lig+1VhmjeCu699tXE/fgFAY0yMzbPKkobyKKIqsNTCckzBzrM4HwraF2Y/uskeGP2/8EPfuCAmffDGpMVABJDitCErGP6MACLkVLL1wwTgCEqNj9CePkgAaU8IloVKwAFyISaAxsAmheghTYXU1KFPrmHMHQ+bhzZaG7q9wLc8FtQ86vrprltbDZNR4rVybkC8PCfMBcpmA5Vu2A9pcCMwuGACFi0naY095igID/gxDcpA1iscTWXk8KCORFXQJ32k5/8xAEg5s8TTzzRdXH66ac/pKsYUoQ6z657jwFYXck1eN+wARg+sFNPPdUBGCf6ssrMBAvA/B5qRGEUXFlJFZ0StC78FAAV4KcaBwDIyTeFEHXGClig5fDuXbSwajHJ4TTG5JvAQj9cXsHNpt+BgwgmZw4vKTRMmWg6rKl+tSyeSjRv/hDUwtqGYefyyy93B7w3vvGNbn3jK47hIs17j+9+97tC/ihJ0H6LiWjul2x4jgFYP6Wd86xhA7CXv/zl8opXvMK9LafnMlMdp0j1l6mI+DhJwsSfpqasspIqei/JpZwiMTtyeuW0TH8ARiqmsZSoopAb42ED5LChplxfiwvNlRwEaMg2C+AAuV4CGag+oGHhKfhysCLgT81jeOn3NkJOI6ZVtGU0w3e/+91Oa2Z8HPyYx8MOO6z2sJ73vOc5TlP9jrWjGFKE2g+tcaMBWA2hNX3LsAEY4fiYf/7pn/6pkE5K5UhxRD4+PdnyQXLaJafFJ0ctKqniAx9RhwR7cFoGwNhsAbVUqJlSo4pSU10d+XCvT+zrBzOoFpeV+F2kxSmfX53xNP1t0p+S9XKYSoHaC9MzgU86HnyWRBITNl9m2vyHf/gHx4cYtn//9393VdRp/Jsct6xAEAOw+itsQv1b075z2ABs8eLFDjwo4RCToMyJEaDB5MfHiU8si+sur6SKzi4bKT4K+sEcpmXeISqGhBaA1J91FaCAVoMfDvnUIUtuYyVrPlwbOU1F4eiqxaGp+SCHtsOBhqTlsg25DXmEfRKVyRgZTwqN2neAKqZn1hOa0gknnCBPfepTex7eueee64gIyBnNspyYCbG+iA3A6suub3dyQoPQFwaP/fbbzzmYyxrRhZy6YfPGnMiHk8XsnVVSRfvWUH2CNwiIABD5yImA5G8iIn3tIC+hWM1hvZi/it4XsxhpAanQDxHlp3WsujDVhSz2mDIZEwAGwDGvflJxaK5suxaZpnCkwo6i2jtEA4D7z3/+cxctyHfX6/wRXUg1Cajg8lIWYkgRyr73Jn9vJsQmpVmzr2HSwPA1waFIuYtnP/vZuXyIvqi0CCWbExsYycVZH2NWSRXtRwMiAD4N2qBf9Qdk9edHgPk+njCPx980/VD0qhsGSd5aQTgFzUJNq6lE+ampLkxxCLU4f65YE7ReqaGyPl3lgiRKVOvN1fzEG7uN9UNgC1G0mG9hm//GN74RFdZfNgjekzWhuZoQckN2gO8PYgPIEGhZpAhlfbf1ewOwtiRbod9hAjBeGwJRTBH4wPIIfX3xYBoEaPh4shjmfS0LX1ao1SlJL0EbaE5sZk0Up8wLYqDvoo1TQc43U7I541cgATYFqig1ZaKx9jOqruiz4BDC3FU11cVSQ+WRMOcR/DZJX1VhO8i9lAMQFgot/vrZz37W5UaGoe5NPGtQ+jAAS2Cmhg3ACGOn4jOciITzlvmbADD8QgBTWcRiyHOYRdLLiZ1kZcpcNJ1f5S+XvI0TgFPzl7LXY4oiH41oS99MWVWLa2q5aj21Lqi0st4BdhQ/p6mp9/QPP1nkvlpROtTiADUOVWiDzFvXGrNqg3CakriMpQOybQI3UsjZa3q+YvszAIuVVIvX9RPAYrPoAQpKqpDV/5KXvKTS22MGPOKIIwSGe3w9RWXWlWUcjQafWVnzAUxJenFm8xGz6QAYACggUfUkX/bsOr9njIAFIc8ESfgRe/gTaHmMGfy8DYBT9g8ODG35+qrISumZANOutNMw34pACUCLP/5hROcq9MU1WaYlS3asH6Jw9cBBojFRiFSNGM/NACyB2e8XgMVm0XMdyciYXCD+rQpgbEh8XDADYKIq4i4khJ7NA9CLMTf6tFNZJL186AQlcHJuY/OvulzUlJlHRJvFmOHXION5YZSev3lW1Qx4HtppG+wfVWWj15Pvx7i6SugOx402SPAP1gN/DbGuQ85D/T/+KNXi8vLiyiwRefLjeyRsXn2VaKpvfvOb5ZJLLulcM6w7503dZwDWlCR76KdfABYbAvuxj33MaTOAxXOf+9zKAMZmRPg8fIgUQswrhqi+K8CGZxFZVdbwgXE9kWqYUTATMlY2ecx0BI9U5RUse2bd3ytVFCkBZfyNRc/IK7LJ5qlRen7dMd/XE2oGaBZouzEVsOu+d5X7UovyY+2yFutog6rF5XFU+pGvoT+uqCAqhzzAb+edd3ZAT4QvGtghhxxSRdRbrv3Wt77lmHI4AAKMeZHCPI/DJ4ckvi98uKk1A7AEZqRfABaThIi5CyaNX/ziF077qgNgiBQN7Mtf/rIz5WVRAanviqANBcsYDUzpfDi1+yS9GiTBxlPGVt+vKSd/iBZD/NrLmGI0AyIz2YjwN2qZG00mrqsZ9DJm7mUzZlOE+igVPw5pDhwM2gL4GO5DvyAqc8aYqFSA+RKt6ytf+Yp885vfrG1hALiYc2inzjjjjEIAY35SCfLJWm8GYL1+hQ3cnxKAcbp7xzveIYTQvvrVr64NYCRVkg9G+HGY08VHjCaFf0zBhg8lJuADfjyisYg4VJJePkZ+TsAGBTtTaGiHAJhGjHU5JoCCTZkEcS3eqaYvvzxLlumLn1U1U8a+q0aetgUWsePQ65AFMmqSrLfqGMJSOhzUOGigOVMtHVM73xMy45BIsFTdxjdqAFZXetXvs0Tm6jJ7yB0xJkQIQPmIaORRERVIuO4LXvCCSk8HCN/whjc4tgnft0Hf5LJgVvSZH7QESlnAx2WXXeaSLAnQ0HwvtEYAgxD1FPxevVAzVRJyhYsJUccMhFkoqymxb5b5iwMHcq0ahl40PA0k6RIswvFhfsZakELdMcYGgwzmQ+WnJCeLb/I973mP08rQpmPM7nnzUAZg7AUcQDnAoK3xPafWTANLYEb6pYFVzaLvRQM75phjXJIlG6bP/s6Hh/kwZIQH1OAvLIpC48SO7wvgQ5NgQ04tORiAxszJRphCyRbdCJXIuC7AazJxFsD5OXGhFpdF3YWM0HTYIHvxDTb56RLhR7WDGOqzJp+b15eaV7E08E2geT3nOc+RX/3qV1Em8hjOwzIA42CIRYNvjqCuT3ziE3LwwQf34/Wjn2EAFi2q9i7sF4DxBllZ9JzsaBCC+q0XADvllFOclsQHiP1eN1LMapwoQ78LUV9FxSrRsDiNAnKAIFoBHzkbKvdhikRD0A20rRD0slXAJqgmzrJr+/H7PHaLpp8dG8DA/KChMi4ON21Td8W8p5LjAl6MJ4UG+wXRkEo5RrFJgi2OPvroxoZXBmD+gwj6AEjhXEypGYAlMBv9BLB+vS6nNXwKmIjwbfFvzIQhw7yOB1s/Pq0sglu9lwANQEoj69B0oL3hw1KfTlYIehYVFP00HbywYsUK54tjo2nLb1R1/siJQz6kM3TdAC3MXmjb+HE0utKn7vLNlP68tcl56Ef5dS0jnq9s/Jp6QdDFW9/6Vsdw0+S6KgIwokMBdg6G/BsNjEMpydMpNQOwBGZjGAEMfjYAhgqvfIiwxBeZjNBcMG+FQRhK0svPMTep3wunNhtfESluFlOGbwLLIvTVTbNq8EJqVFEsa8ximF1x9tc1HTb5eSh9FeClfHt+/1nM9TpfWdRdobmyzoEEcza+Lw5ade5vUj7aF+ZeLAjICZm9+MUvlpNPPlkOOuigRh5HsUoAkTQWAp9YHxdccMFDOA8B9Re+8IXueQAqkcmMIbVmAJbAjAwjgMGSTagvwRx8JJysMf/lNRKQ2azCIAOfpFeLU+LcxuTYRHFKDWvWjdIHuKzgBX/T9HOs0HTQILNY9LtYYhpIgvZbFBjTz7GRYA6oEmxTp4VsGWjdvsYNACp1l29OVq2O+fKb+uIIMmqTcqzKu/I+HPwUUH/yk5/Ieeed5xhxUjiEVHmXflxrANYPKZc8YxgBjFMtYb+vf/3rXY5PWYQgTmr+wBChTROd0bLYfPij5SQ4NfbDXxEGL/gAp+wLjJd/oyUypq79cIwH+WOOTSWQROctj5Gkqc8wzLPy5yuk7uL/mKdZc0UFNpsaW0w/mNkx96KhsqawYFBYMgVatJjx9/saA7B+SzzjecMIYGhURx11lLzyla+UZz3rWaVgQ+ADZkSCPmia6AzwsblgOtQTM5pcKsmVbJBE1EGyGoai+wUb++WHQ3ZoOoC/Bs8ksMSTAVSl7sKvgy+OiFb1xYUFNrPy4pr0QYXzwgFOTb787uyzz3bpIe9///tTmMIkx2AAlsC0DCOA6QZ65plnulMk5rWihjmI0ujQROWR9BLByAbka2ldTp8yhOPby6PL6qcfDlloja+2NZ0qcldNOpUQdcYOnyDBLaHP1Z8v30SpQUJqpsQsm3UoIbWjjqlPKaxglyH3ElPrYYcdJuRu1iE4jqWLiiX3rjLf/bzWAKyf0s551rABGB85bPSUqv/2t7/tTFllPgZAi0AP/FpZJL180DfffPPDCFa7nD4lIu6VKqopPxybIDJEQ80KkuhCVhpRl5IvLqyrVVUuPnVXmBenZmUsBlkAl5fegfWBvpSVRNlwXvWqV1Udnrs+hi4qlty71gD6dJMBWJ8EXfSYYQQwgjj4COFD5ASZFR7vy0RPoARBqC+MTYATrdIgpbQJEkhCgEkM/VWvSyzGD4esNDcOGabgh+O9MdNxeFEKq15l0ev9miDs05j12md4v08HFVb6VjMlpkidI3y75DaifSn34XHHHddI2HxRqHwMM0/Tsmm6PwOwpiVao79hAzAVAWG/H/nIR1wQRwxHIR8UgMWHzIbMn6YY3WtMS+4tnLIpSZJK4isbJvlV5KBhziRgost8OBUcBxHSHVIJ42dcaDr4V/FZdtl8fykyInoSvxyHPuQG6OMPRpv+8Ic/XLtuWxGAxZB7dymjmGcbgMVIqeVrhhXAyCM59thjnfaVx8GnouWDhmmbzQ6NTYtT4hcDyMrub3mKtnQPWBDhR3RfKhF+qlWwKcNdl6URhAEmbeXD6bOVASQVkGdcGglJiHoKhTwZk5aTYUz4zvBJASznnHOOK4RKUAcglNV6pYsyAOvXrrHpOUbm26C8y5y3X/3qV+X00093QRNk4xMRVdUJTwg9/G2EABedeHkG/jI+Zp6BE5sTKRxsUOrwszqO8QbFtaUrNhW0Ha2M28YzqvYJiwmA0UtwS1N+OB07Bw9MZKnkxTEu1hiHqTJzdlX593K9ckKicQGwBDx973vfK8yZrPI8MyFWkVa71xqANSTfGOctpKGYMGC/+PGPf+wK4F1++eWVRnDSSSc5pzT9FCWvcsrEz4WmRcQaTU0qmB7RyDQxFSd4V4wJACybYEpUUQQk4LBnTG3KJdYPp7l5hH8z70rm2/UBhPEQBJSSORNm+TvvvHNLusNZZ53leDT/9V//tdJ3VnRxEYBVJfdubFANdmQmxAaFWberfpsQqzpv+fjxS6F9VGkf/ehHneZEZCEbR1YjGILwePrXZGU+LHxMnN4x9fgsGVn1q3z6pzY4Dhk3oM+Y2JRTKZgJqFA9mMNBnVDrKnNZdq0GLmh+FVqOanVd5cPpmFVOpGj0I/m9TFb8XgmE+S5Ys4AZxWP5NstSTmL6j6GLop8scu+Y/lO5xgAsgZnoN4BVtX1T9A6qpM9//vOVpIUZElMSpc+zqi37JL1aUh0tgsg1QKLI/ATIhfRP/J8+NVcnBDb9f51kVPKGuL+IDquScBq4GDottNaUWBo4jCDf0GdZlA+nc8Z9WWS+VXkpQ9FiYqUR4JJKw+pAMJCmYPzzP/+zLF682CX+W4uXgAFYvKxauzJlAPvFL34hb37zm12ARdXcInjcvv/978uLXvSihwFYHkkvPi9yvtDIejE7cfoPQ5g1MZVna4HGLJALHfyYNdE+U/LFaXkZwvh7kVOTi7pXc2bTfjjeLeQWbPJ96/alwSQUowS0iR4FwC666KJWzcB1x5vyfQZgCcxOvwEs1oQIqSiRhPjA6oQd46AmEIRKrvho/I2WkzraFrxvStKr5UgwObYdJabJqFlanJL44m9jbAAqARKY6VRT7BI00D5/+9vfJhPGryYxxtSmibWKH041OcLm0eSJGO1yzvxtBp8lvmWKnvJOfGP4vQ444IAEdqPBGoIBWALz1W8Ai3HeYuIgIopE5AMPPLCWlNg8KIr53ve+11FEKSipRsNm5/u92ADRvLr25+iGjMamNccAW6UTUrYFn07I1+R8lvpagiu5KbXkYIZLgATA3ysrSS/yUj+cHkrwKxExSlRr1344fa+QBQQfFFGHX/nKV5IB2F7moN/3GoD1W+IZz+s3gDGEssrMr3vd6xwNlPpXAB8Apkpj0+BU+clPftJpMGzybC7kURF4AADwR3OrFi1a5MhVU2lF4elKCuvz5YW1q/BP+WU9mmDHSNGcqdGZKdXUAkyvuOIKF0DEPNC69MPp86+88koXmUtyP98Hh0TM7HXTDUh6ftnLXuYOEPgdKWGEdhc2fodfGZNlnW85lW8yHIcBWAIz0wWA9eO12TDwG33hC19wVEJEV2FWpP4SH7AmK0Ojg/lQmej7MbayZ/RacyyLTihkx+D98wAuKyRefSf+plz2Hm3/nvckOpNNOSuJuu3n5/VPgAuyrQoMbfjhdIzkNXIA0ZQSqpazJkhRqdv+5V/+xRFJv+td75LTTjvNsddjts8CMA6gqVRxqPu+BmBNSa7BfoYVwBARpkPMkGxumHQAMWz/WlkZEw8RfmzKdaIDG5yGLV31gyrKL86YxZfH732+PDZjcoaQHblxbeZ8VZEphw+omfbaa68qt7V6LYchzY1r2u9Vxw+H5s16p9aX8nkCZM973vPksssucybOug25X3jhhc5ywfog74vvyQCsrkTbu88SmduTbWs977///sJJkw2Zjx9TopL09gMoqr6YsoJgzgQsumxapwozJfXVHnzwQXcA4P8KcBqsEEZT9uMwAPCyKWM67MfzYuZCNUKCjtDy+91CP5yamDH14XtGs4fbEGDFPA+I8TepJnVkCIMHfdJ4NuZD/b//7qQQcIjkGW984xtdYNUwNDMhJjCLw6yBkZx5/PHHOwc/p08l6dXSH2gTKVH7EMaPGaZu2fs2lpOy8Yc1vvxUgTCaUnPh8gCu1yhPnT8237xaaG3IoqxP0h3QwFLSCPF1YTonbJ4Gy82//du/ydvf/nbHQs8fzH55WnUR5yHlVnzAAsBYv2FDLnxrmDGf+cxnukPlwQcfXCbO5H9vAJbAFA0zgGk9o2OOOcZtKur3IkCCE6nWP0pgGhwXIwEmqWkUbH444asChfpzwsKMgJ2mChQBXJH5DaBn40yJEzJFsl7WNXleaPQc1DhYPP/5z5cPfOADst9++/W87GNNiP6D8LkR6XvCCSf0/PyuOzAA63oGNqn+GxMYRuND4LXY4J71rGfJ4Ycf7hzI2PsBLnwA0OgQhZhCY2PByU2dqC5MT3kyaNPHlOfPAeCYI1pWqgBmKIA+parPjJX0AkC+a9OvP5f4eMl5fMITnuDMhueff7784Ac/cH7hJvxz73znOx3BgAZxYKr80Ic+9JDlxMGMuSYKkX+jgZ1yyily6KGHpvDp9TQGA7CexNfMzcMKYFBP8ecFL3iBHH300Y5tG80LWiqCO/i/bpRhNJ5f7K8ZKRf3kiJVVNfkwZoqEAaZcPjQcOw2UgXqzDfaIBWyFSjq9NH0PVrmhuhaNB5MiU972tMciJHA30Qjyf4f//EfXdkVzLmE0QPiaMikwpAug1xIlqbxvb385S+Xk08+uYnHd96HAVjnUzC8Ghi+iE996lNy3nnnOQczf9hoyA3TYn18dPAL4mDmAw/zqnyAU5DzAxbw5fR6kiU6Ek0nJaZyTsyEp2MiSkkjxIdCQMm+++7r5pNDSFYunCYOV00VqPM5KlkvY+oloq/Os4vuISoQDQytnvbxj3/c8R8aRvyBAAAQKUlEQVSi/VhrRgIGYM3IsadehlUD84XCZkd5FfUBoImRfMnJkb/ZGLkGXwGApn8U4Ii2UiYMXyMIWTF8cIuhfWKjJbk0pdwq5MapmUbOXCoNWWNmjZVVVqqAP3e8FweQrFy4KlUFqGjMQadLFpBwjsJEatY3vi/C5lNhxE9lXfUyDgOwXqTX0L3jAcAQFeS+RFTlRVsBbnzogJsCHJtTFsCRoArIAXD88TU4XyPIo33SOlU42Lm/KlFxQ1Of2Q3h8pobl0q+FwNFVsipSR+TpgqEUZRhqkCYJgDAYcbkut///vcuwi8lWeH3QvvU6gVvfetb3do/8sgj21w6465vA7AEprwrACuryswJmhB47OiYZs4991wXCt9VywI41eAwazFeAkVCDU4Bzjd3sWHiJ8CHo5RWWcz0bfMaZp3clROyibpQTc0VvhbMrP1m5C9LFWAe8S9xgAnnr9dUgbqyCxnw4dM88cQThcoOKYFs3fdL6T4DsARmowsAi6nKDHCRL8LfVGMGzKpWZe6neAE4AgyyNLgQ4DjBY84h/4YQdS3pHvpzfA0uywfXNMClGEyCeY7CmQRIIINUGnPNIYTk+DqpAsxdGw3AIucKbZU1ecQRR7h1llUTr43nj6c+DcASmO0uACympAoZ+1DTqNnDzzlJQGyVh6AA9+c//9lFaL30pS917BaYKe+66y632eRpcCSIapCJbpactBXg0OTQAEIfXBWAIwQac2lKkXQImahRQrDZlFNpHMAUVItSMeqmCjCPVeZO5UISMetJK5BD1Es5IqwXVYKNBs060tW6MADrSvLec7sAsJiqzLBokF9CpVjaM57xDHeSJP9nkNvFF1/sTu6wePuNzY6IRF+DA1AU4DBRcqpWEyV+OPXBEbocAhxAh9mSpgAXanH8nI1Na3xpiflU5MuGjDxSA9Xrr7/eybTXCtlhqoDviwsPJ2Gwic6dzhV9AaqwuCjlF2zzWDAgs45tw2gdiX33qtcZgFWVWAvXG4C1INQWuswCOMBNAY6NRwEOYAsBLvTB+QDH7/Azcr+vxYWbZAuvldulajn4vVKKnCM/joASTHJVtJo6sgu5DX2A08MJmhry4f9cjz+OtfJf//Vfbnzvec97Kj16PFpHKgnIu9gArK7kGryvCwCzj6TBCdzcFZsWwQ5ZGhw5QWxuaGqhBgerBTlzmDXR4rI2yayEYWU5b2sTpyQJ5rletZwmJY0MSXvA75VC+RZNFdBq4phZ8a2ec845LpKU/zPn0EZR7iSmjWfrSIx8/GsMwKpKrIXruwCwmKrMP/zhD10xSg3iOO6441yRQGv1JJAFcJT9wE/Chgx4KcCFGhyamWpwvg/ON1E2WTxTQ/kxF7cFkHWkyEGAZPiUasfxHtdee60zG6qf8C1veYujasJMzXg52MTmqRmAxa8MA7B4WbV2ZRcAxsuUVWXmdHnssccKDmXMW5wqB93/1dok1uyYje6www5zXJEAHIEceRocJr0sDQ6wI/gEMFMNLqt4ZhhgAuChYYUApbyQ8FgSop5K00Tq1DgYQ5MmeWkk7f/85z+vFTZv1pH4FWcAFi+r1q7sCsBaeyHrOFoCAE4soXEMwBEtqQnevg8OgMtKGs6ifFq+fLmLwIMFJAvgol+u4QvRVkl3oHhjSg3A4hCB7JkjanxR86vuYc+sI/GzawAWL6vWrjQAa02046pjNk+NGlQmE42iJOoSDU4BDpDzAQ4KLwCOzZhriYbEVFnEaahsJv0wMcIpSOQhifT9eF7swsE0SK0tyKlp3/ve9+SnP/2pfPGLX+xpnGYdiZsBA7A4ObV6lQFYq+K1zjdLoAjg8C0BYJgwn/KUp7g6bVkA5/NRYqYMAS5ME+D/vQJOGJ6eyoQqiTDgBZgjG9jmMbmnpiWmIrOmx2EA1rREa/Q36AAGxdBRRx3lWMrZrChXDmuH31KjpaoxTUN/y8c+9jGXSP3KV77S/e3zUaKVYdrChBeaKAG6bbbZxgFg6INTTkMNNQ8DTTBRltErQReGf49Al5Qa4+KdNTjjjDPOcOTE+L+s9UcCBmD9kXPhUwYdwDi98wfzDv4T2MoxpfjVegeNliqBZdH3IRB0cOCBB+bSRXEIURNlFsBhoqT0i89FCU1XFsD51E/0mwdwCOEPf/hDUlWyGZNWf4ZEGFJhmFyouQXVWkp0W31fRH1+oAFYnwWe9bhBB7DwnSgbQfQilV+1DRstVQLLJrkhKMABbiHA4SfKAjgtl4MGh4YXmijhO9ToyayipzEaXBuCgl6LPDRMhbz3m9/8ZoG5Bnoya/2TgAFY/2Sd+6RhAjA2roMPPljgG/QLMQ4rLVUCy2dghhADcHAuqgaHlgNQfOhDH3ImyhDgFOzoFy0o5KIE8KrUFYsVJEnLRERqjtxVV13l2DZ+9rOflZpD/WeU8R1eeOGFrobYLrvs4m570YteZMUwg0kyAItdtS1eNywAxod9yCGHuHLlfGx+MwBrcQENSddasZtDEInB73jHO+Q5z3mOqxGHBgeA+QCn2huAR42yGIDLSvYu88H54mWMABZ+L6WMIofvox/9aKVSQzF8hwAYfrXzzz9/SGa4+dcwAGteppV7HAYAw5kNSD372c+Wt7/97Q+TQb9MiDEBJV/96lcdKTGbERvi2Wef7epcWUtHAmzeaPGYorX5AJdlogTASLz2q3kryAFwgEZYLscvnBmaKvX/PsABpvzZZ5993LC+853vuDpfX/jCFyoJLyZZ2QCsXKQGYOUyav2KQQcwNpZXvepVjiWCSLas1i9aqpiAkl/96leOioicKEpdnHrqqUnXOWt9AQ7JA1iH5Itl+eBuu+02p6GFAKdghy+rDODwtxHEwj0QOHP4gUmFSuNVq1TH0EUBYFgydthhB0dRhTYG0721v0nAACyB1TDoAHbJJZfIQQcdJPvuu+8WH8AHPvABIcyY9qY3vclpO13QUmUFlPhTzobEaRoTlbXhlkAMwMFnmKXBAXCf//znHYDsueee8pnPfEZY90QfwlMJ1Romz9B0nifRGACDjxLtD9AlipfUFAiWrRmAJbUGBh3AkhKmN5i8gBJ/vJxqCRRgc7I2viUAwAEaWRocOXEccijqSloAoEUQBmVd0MzgQ9QoyxgpxpgQw35ISfjtb3/reC+tbZKAaWAJrAQDsOYnoSigRJ+G74LwZ07SbEhNthhfnD6PIogHHHCAfP3rX5eXvOQlTQ7D+mpIApS6gXSZoq4AHJRbANZrXvOaWk+I4TtEuyP6EnIAqkCwNjBd9spsUmvAid5kAJbAxBiANTsJZQElPO2Pf/yjSzzFB4ZJqOkW44vjmWyC5MsRHcdmaADW9Ew00x9h83vvvXej4FHGd0gpIwKMYPcgoOTMM890iebW/iYBA7AEVoMBWHOTEBNQgm+OUu9f/vKX+7Yh5PniCHqBhQItjChOA7Dm1oL1NPwSMABLYI4NwJqbhJiAEsxB3/72t10JDBonXHwLbbU8Xxw+lZe//OUuDBvtywCsrRmwfodVAgZgCcysAVgCk9DSEIp8cdAOEbm2//77y6tf/erWACzWH0fY9tve9jZHUEugwC9/+cuWpGLdmgSakYABWDNy7KkXA7CexJfszWW+OCiCMHnSlixZ4kKxP/vZz8oLXvCCRt8pxh9H2Xv8K0TWEUZOsu7WW2/d6DisM5NA0xIwAGtaojX6MwCrIbTEb4nxxfmv0KYGFooqyx/3qU99yhWyfP/735+4ZG14JoG/ScAALIHVYACWwCQ0PIQYX1wXAJbnj1PTIXlNlMQhaZYab9Z6kwC+TbgM0Wahxgqb1cnrTb4GYL3Jr5G7DcAaEaN1UiKBIn8cLCkEssCoTqVl8tKg/2ojxWA8TdRFF13kmDQ4DGQBmNXJ6201GID1Jr9G7jYAa0SM1kmBBMr8caeddpoDrve9732ul9e+9rVy6KGHNl7fKiagBD7DV7ziFY6KjITfE044QY4++uiBnV+0XiJMswCsXyTXAyu8koEbgCUwswZgCUzCEA8hxh9Hoi5a2AUXXOCqDVNpGGYQZV1vSjwxASXwaAJiVAygoCX0TbBSTJ06talh9LWfIgCzMkO9TYUBWG/ya+RuA7BGxGid5Egg1h/34Q9/WM455xxHIEuuHH6xtltWQMkHP/hBQVM766yzHG0TTCXUB6tSt6vtcVfp3wCsirSqXWsAVk1erVxtANaKWK3TxCWQF1BCEMkRRxzhSJb59ze+8Q2haOSgNjMhtjdzBmDtyTa6ZwOwaFHZhUMigaKAEkqNXHrppY7774YbbnAa2B/+8AeZPXt2429PQcuDDz5YxsbGnL8NKi/1A+rDeo0ULAKwftXJa1xwiXRoAJbARBiAJTAJNoS+SaAsoARt613veperMUeDt5IgE/xyTTfAiVIoRAoyrsWLF8vHP/5xx46irZdIwSOPPFJgOCFRHWZ5wJHn0Lqsk9e0HLvqzwCsK8nbc00C41MCE0TkSyJyn4jkOdnOFpG7ReRUEdlGRK4UkcdBWNKyyGaKyCUicoyIXO496zMicqGInLf5Z9eIyFNF5M6Wx2PdD5EEWPjWTAImgcGWwGIRuVhE/iQiGza/ykki8sjN//60iDxCRM4Vke2oWSgip4nIf7T42pNE5HcisruInCUiJwbPOn/zGAA32s82X9MeA3SLL2tddyMBA7Bu5G5PNQmMFwnMFZHvishbRcSnzTAAGy8roMX3NABrUbjWtUnAJOAkcIqIjIrIGZ48zIRoi6NnCRiA9SxC68AkYBIIJLBIRIiquF9EZojIT0TkdBFB69JGDP+xInKYiOwnIv9PRJqPKLGpGWoJGIAN9fTay5kEOpHAYzcHleAHmygi3xSRfyVIcPNo8Mmx93xSRA7drJ3Ba2X+r06ma3AfagA2uHNnIzcJmARMAuNaAgZg43r67eVNAiYBk8DgSsAAbHDnzkZuEjAJmATGtQQMwMb19NvLmwRMAiaBwZWAAdjgzp2N3CRgEjAJjGsJGICN6+m3lzcJmARMAoMrAQOwwZ07G7lJwCRgEhjXEjAAG9fTby9vEjAJmAQGVwIGYIM7dzZyk4BJwCQwriVgADaup99e3iRgEjAJDK4EDMAGd+5s5CYBk4BJYFxLwABsXE+/vbxJwCRgEhhcCRiADe7c2chNAiYBk8C4loAB2Liefnt5k4BJwCQwuBIwABvcubORmwRMAiaBcS0BA7BxPf328iYBk4BJYHAlYAA2uHNnIzcJmARMAuNaAgZg43r67eVNAiYBk8DgSsAAbHDnzkZuEjAJmATGtQQMwMb19NvLmwRMAiaBwZWAAdjgzp2N3CRgEjAJjGsJGICN6+m3lzcJmARMAoMrAQOwwZ07G7lJwCRgEhjXEjAAG9fTby9vEjAJmAQGVwIGYIM7dzZyk4BJwCQwriVgADaup99e3iRgEjAJDK4EDMAGd+5s5CYBk4BJYFxLwABsXE+/vbxJwCRgEhhcCRiADe7c2chNAiYBk8C4loAB2Liefnt5k4BJwCQwuBL4/22Xhu/N6RkOAAAAAElFTkSuQmCC\" width=\"432\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function matplotlib.pyplot.show>"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy.plotting import plot3d_parametric_line as plt3D_par\n",
    "t = symbols('t')\n",
    "x=-2+3*t\n",
    "y=3-t\n",
    "z=t\n",
    "plt3D_par(x,y,z,(t,0,1))\n",
    "show"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El conjunto solución corresponde a una recta en $\\mathbb{R}^3$, la cual coincide con la intersección de los planos."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}