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diff --git "a/Chapitre 1 - Systemes equations lineaires/1.2. Nombre de solution d'un syst\303\250me.ipynb" "b/Chapitre 1 - Systemes equations lineaires/1.2. Nombre de solution d'un syst\303\250me.ipynb"
index c28ebd8..8e6471c 100644
--- "a/Chapitre 1 - Systemes equations lineaires/1.2. Nombre de solution d'un syst\303\250me.ipynb"
+++ "b/Chapitre 1 - Systemes equations lineaires/1.2. Nombre de solution d'un syst\303\250me.ipynb"
@@ -1,593 +1,95614 @@
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"# Concept(s)-clé(s) et théorie\n",
"\n",
"On considère un système d'équations linéaires aux inconnues $x_1,\\ldots,x_n$\n",
"\n",
"$$S=\\left\\{\\begin{array}{ccccccc}\n",
"a_{11}x_1 &+a_{12}x_2 & + &\\cdots &+a_{1n}x_n &= &b_1 \\\\\n",
"a_{21}x_1 &+a_{22}x_2 & + &\\cdots &+a_{2n}x_n &= &b_2 \\\\\n",
"\\vdots & & & &\\vdots & \\vdots &\\vdots \\\\\n",
"a_{m1}x_1 &+a_{m2}x_2 & + &\\cdots &+a_{mn}x_n &= &b_m\n",
"\\end{array},\\right. $$\n",
"\n",
"où $a_{ij},b_i\\in \\mathbb{R}$ pour tout $1\\leq i\\leq m$ et tout $1\\leq j\\leq n.$ \n",
"\n",
"---\n",
"Un système d'équations linéaires à coefficients réels satisfait à précisément une des conditions suivantes.\n",
"\n",
"1.Le système ne possède aucune solution.\n",
"\n",
"2.Le système possède une solution unique.\n",
"\n",
"3.Le système possède une infinité de solutions.\n"
]
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+ " <script type=\"text/javascript\">\n",
+ " window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
+ " if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
+ " if (typeof require !== 'undefined') {\n",
+ " require.undef(\"plotly\");\n",
+ " requirejs.config({\n",
+ " paths: {\n",
+ " 'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
+ " }\n",
+ " });\n",
+ " require(['plotly'], function(Plotly) {\n",
+ " window._Plotly = Plotly;\n",
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+ " </script>\n",
+ " "
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"source": [
"import Librairie.AL_Fct as al\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import plotly\n",
"import plotly.graph_objs as go\n",
"import pandas as pd\n",
"import random\n",
"from IPython.core.magic import register_cell_magic\n",
"from IPython.display import HTML, display"
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"### EXEMPLE 1\n",
"\n",
"Nous allons travailler avec un système de $2$ inconnues, $2$ équations:\n",
"\n",
"$$\n",
"\\begin{cases}\n",
"a_{11}x_1 + a_{12}x_2=b_1\\\\\n",
"a_{21}x_1 + a_{22}x_2=b_2.\n",
"\\end{cases}\n",
"$$\n",
"\n",
"On utilise *la syntaxe suivante pour entrer les coefficients du système*\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"A&=\\quad [\\quad [ a_{11} , a_{12}, \\ldots, a_{1n} ], \\quad [ a_{21}, a_{22}, \\ldots, a_{2n}]\\quad, \\ldots , \\quad[a_{m1}, a_{m2}, \\ldots, a_{mn}]\\quad]\\\\\n",
"b&=\\quad [\\quad b_1, b_2, \\ldots, b_m \\quad]\n",
"\\end{align*}$$\n",
"\n",
"---\n",
"Entrer le système ci-dessous - ou n'importe quel système de votre choix. Après avoir étudié les deux droites, entrer une solution du système\n",
"\n",
"$$\n",
"\\begin{cases}\n",
"-2x_1 + x_2=2\\\\\n",
"2x_1 -2x_2=1.\n",
"\\end{cases}\n",
"$$\n"
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"al.bgc('seashell')\n",
"#Par défaut, les coefficients sont fixés à 1 et n=2, m=2\n",
"\n",
"A = [ [-2,1] , [2,-2]]\n",
"b = [2,1]"
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+ "yaxis": {
+ "automargin": true,
+ "gridcolor": "white",
+ "linecolor": "white",
+ "ticks": "",
+ "title": {
+ "standoff": 15
+ },
+ "zerolinecolor": "white",
+ "zerolinewidth": 2
+ }
+ }
+ },
+ "xaxis": {
+ "autorange": true,
+ "range": [
+ -7.33608195902049,
+ 8.33608195902049
+ ],
+ "type": "linear"
+ },
+ "yaxis": {
+ "autorange": true,
+ "range": [
+ -8.02547770700637,
+ 8.02547770700637
+ ],
+ "type": "linear"
+ }
+ }
+ },
+ "image/png": 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+ "<div>\n",
+ " \n",
+ " \n",
+ " <div id=\"3f3b062a-dfff-454e-9ee8-c4bfdfc7890b\" class=\"plotly-graph-div\" style=\"height:525px; width:100%;\"></div>\n",
+ " <script type=\"text/javascript\">\n",
+ " require([\"plotly\"], function(Plotly) {\n",
+ " window.PLOTLYENV=window.PLOTLYENV || {};\n",
+ " \n",
+ " if (document.getElementById(\"3f3b062a-dfff-454e-9ee8-c4bfdfc7890b\")) {\n",
+ " Plotly.newPlot(\n",
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+ "if (outputEl) {{\n",
+ " x.observe(outputEl, {childList: true});\n",
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+ " })\n",
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+ " </script>\n",
+ " </div>"
+ ]
+ },
+ "metadata": {},
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+ }
+ ],
"source": [
"al.printSyst(A,b)\n",
"\n",
"al.Plot2DSys(-7,7,15,A,b)\n"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 4,
"metadata": {},
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"source": [
"al.bgc('seashell')\n",
"\n",
"alpha=[-2.5, -3]\n"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 5,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "La suite entrée est une solution de l'équation 1\n",
+ "La suite entrée est une solution de l'équation 2\n",
+ "C'est une solution du système\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "True"
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"source": [
"al.SolOfSyst(alpha, A,b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### **EXERCICE 1**\n",
"\n",
"Pour chacun des cas ci-dessous, déterminer la/les solution(s) des systèmes. \n",
"\n",
" $$ \n",
"a)\\quad \\begin{cases}\n",
"\\dfrac{3}{2}x_1 - 2x_2&=0\\\\\n",
"-3x_1 + 5 x_2&=3\n",
"\\end{cases} \\hspace{1cm} b) \\quad \\begin{cases}\n",
"x_1 - x_2&=\\phantom{-}2\\\\\n",
"-3x_1 - 2x_2&=-1\\\\\n",
"2x_1 + 3x_2&=\\phantom{-}4\n",
"\\end{cases}\n",
"$$\n"
]
},
{
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"metadata": {},
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"source": [
"al.bgc('seashell')\n",
"#Par défaut, les coefficients sont fixés à 1 \n",
"#Attention d'adapter les valeurs ci-dessous pour a) et b)\n",
"\n",
"\n",
"A = [ [1,1] , [1,1] ]\n",
"b =[1,1]\n",
"alpha=[1,1]"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 7,
"metadata": {},
- "outputs": [],
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+ "data": {
+ "text/latex": [
+ "$\\begin{cases}x_1+x_2=1\\\\x_1+x_2=1\\\\\\end{cases}$"
+ ],
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+ "metadata": {},
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+ "text": [
+ "La suite entrée n'est pas une solution de l'équation 1\n",
+ "La suite entrée n'est pas une solution de l'équation 2\n",
+ "Ce n'est pas une solution du système\n"
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IzKxI+/ceBKZ/mTLRjQnwCUzDG4LANATI8SAIIDCDiNnKkAhMK1i9L4rA9D5iawMiMK2h9b4wAtP7iK0NiMC0htb7wghM7yNmwFUEEJiGVwKBaQiQ40EQQGAGEbOVIRGYVrB6XxSB6X3E1gZEYFpD631hBKb3EVsbEIFpDa33hRGY3kfMgAjMdO8AAjNdnlTzkwAC089cs5gKgZkFZf/egcD0L9OsJkJgZkXav/cgMP3LNKuJEJhZkfbvPQhM/zLNeqKTp8/p0cd/X499/H06fHBf1q/f9vv4BOa2kZUfQGAaAuR4EAQQmEHEbGVIBKYVrN4XRWB6H7G1ARGY1tB6XxiB6X3E1gZEYFpD631hBKb3EZcN+PTzx/STH3q87Pfe+faj+sRH36vGxvpEMFYLzM98/omlOh/5wHsS1Vs5NDQypkc/+QX9q3/5Y6mKUQSmUSwSAtMQIMeDIIDADCJmK0MiMK1g9b4oAtP7iK0NiMC0htb7wghM7yO2NiAC0xpa7wsjMN2LeHhkUc++sKgr41J3p/Sdb6lOrcmSwPzM7z6hzz3+YXW2ty7VLQnHp587VvZ7Ji80FZhTUzP65V//ov7qq09q3+5u/d6nfgGBaRJI2mcRmGkTpZ6PBBCYPqaazUwIzGw4+/YWBKZviWY3DwIzO9a+vQmB6Vui2c2DwMyOtW9vQmC6leil/kU99pm5JXm58uvwLVV69OdrU2l0PYG5IjFL/1n61OTKJyr/ydvfqk/+1p/onruOLMnNoeExffBjn9a5iwNlYvH6T2AODI+WfcJz5dOdpdorUrL0f//Kx35KP/KO777hTHwCM5XI0y+CwEyfKRX9I4DA9C/TrCZCYGZF2q/3IDD9yjPLaRCYWdL2610ITL/yzHIaBGaWtP16FwLTbp5/8dfz23rBy8cX9fKJxTVnHnmwSnt2VW25Vkdblb7nO9Z+cnMjgXn976+Iyh/6vqPXvgZekok/8/Hf0Ed++j16+N47VXr+0ce+sPTpyNKv63dgrv4E5sonKvfs6l6qt1UxudXntgxl+UG+Qr5dYqueD0Fgjr12UWN/+mdqHnxNc3XNmi58h/b/+A8akuN4SAQQmCGlne6sCMx0eYZSDYEZStLpz4nATJ9pKBURmKEknf6cCMz0mYZSEYFpN+k/+r/n9ff/bcHuS9ap/hP/Y822BGbpU5S/9jtf0mO/+P6lT1qu/qE8q8XnipQ8+kCk+6IjNxSY6/2Qn5LkvOXAnht+ChOBmfm12doLQxCY4x/5oHZOniwDcvx7PorE3NoV4SlJCEyuQVICCMyk5MI+h8AMO3+T6RGYJvTCPovADDt/k+kRmCb0wj6LwLSbf14/gbmewHziL79W9sN+ViTkVgTmylfPr6e92dfIEZh272bi6r4LzIFvvaKb/uBn1/A50/6Auh7/t4m5cTAsAgjMsPJOc1oEZpo0w6mFwAwn67QnRWCmTTScegjMcLJOe1IEZtpEw6mHwHQra5d2YD728fdd++E5pp/AXPl058oPDtoKdQTmVihV4BnfBeblr7+gg//h6m6E1b9G6nZpsLtXc7dEarq7oK4Hbq1AArwyDwQQmHlIyc0eEZhu5uJ6VwhM1xNytz8EprvZuN4ZAtP1hNztD4Hpbjaud4bAdC+hSv8U8vW+8r2yA/M973rb0te+b7QD88tf+bqefDa+9mnN1TswS8RL7zh+6qx+8G0PbxgAAtO9u7nUke8Cc/yNfu187MfX0J+talDd4nTZ709V79Dljl5N3hSpvlBQ91si1TSk8xO3HI2ftrZIAIG5RVA8toYAApNLkYQAAjMJNc6UCCAwuQdJCSAwk5LjHAKTO5CUAAIzKbl8niuJx5/80ONlza/8pPDGxvql319PYK78/mY/hfzwwX1LP6Sn9AN/XnjpVW30U8j37e5e+gFApedX/1oRnn/11Sev/dHqHk3o80N8TOgFIDBLeM789h/r9r4/vEbqctNhLfzcJzQ3PqWJ54uqORmr83KfOmfOrqJZpXOtkcb3Rqq+I1LnwwU17mw3JM7xPBJAYOYxNTd6RmC6kUPeukBg5i0xd/pFYLqTRd46QWDmLTF3+kVgupNF3jpBYOYtMfo1JYDANCTo+ycwV/CUPolZdeGSZmvr1H7/betSG3/jskaeKUrHY7VeiLV74pU1z/U3HtLI7kgLRyK1PhCp7chewwQ4ngcCCMw8pORmjwhMN3NxvSsEpusJudsfAtPdbFzvDIHpekLu9ofAdDcb1ztDYLqeEP2lTQCBaUg0FIFZwtTT1qCxyVlNzy5sidrMyIQGnypq/lisprOx9oz2qXZxtuzsSN1uDXZH7NHcEtH8PoTAzG92le4cgVnpBPL5fgRmPnNzoWsEpgsp5LMHBGY+c3OhawSmCynkswcEZj5zo+vkBBCYydktnURgbg9g/zeKmoqLajgdq2eoTzvmh8sKTFW36FJHpOmbItUVInUfLaimnj2a26Ps3tMITPcyyUtHCMy8JOVWnwhMt/LIUzcIzDyl5VavCEy38shTNwjMPKXlVq8ITLfyoBv7BBCYhowRmGYAh+LTN9yjuagqnWePphlkB04jMB0IIactIDBzGlyF20ZgVjiAHL8egZnj8CrcOgKzwgHk+PUIzByHV+HWEZgVDoDXZ04AgWmIHIFpCHDV8StvXNboJns0Lzce1ujuSIu3FtRyP3s0003ATjUEph2uIVRFYIaQcvozIjDTZxpKRQRmKEmnPycCM32moVREYIaSdPpzIjDTZ0pFtwkgMA3zQWAaAtzk+NU9mrHmjxXVfDbW7hvs0Zw9FKn57khd9x+x2xTVt00AgbltZBxYJoDA5CokIYDATEKNMyUCCEzuQVICCMyk5DiHwOQOJCWAwExKjnN5JYDANEwOgWkIMMHxy98oaqavqPrX+9QzFG+4R3PqpkgNUaSut7BHMwHmVI8gMFPFGVQxBGZQcac2LAIzNZTBFUJgBhd5agMjMFNDGVwhBGZwkac2MAIzNZQUygkBBKZhUAhMQ4ApHB/qO62JF2LVnIzVeTlW58zZsqpX92j2anxfpOo7Cup8qKDGne0pvJkSWyWAwNwqKZ5bTQCByZ1IQgCBmYQaZ0oEEJjcg6QEEJhJyXEOgckdSEoAgZmUHOfySgCBaZgcAtMQoIXjV16/rNFnY+l4Ua0XYu2eeGXNW97coxkt79HcY6ETSq4QQGByF5ISQGAmJRf2OQRm2PmbTI/ANKEX9lkEZtj5m0yPwDShF/ZZBGbY+acx/cnT5/To47+vxz7+Ph0+uC+NklZrIDAN8SIwDQFmcHxmZFyDTxWX92j2ac9orJrF2bI3j9Tt1mB3r2YPFdR8T6Su+9ijmWY0CMw0aYZVC4EZVt5pTYvATItkeHUQmOFlntbECMy0SIZXB4EZXuZpTYzATItkPuo8/fwx/eSHHi9r9p1vP6pPfPS9amysTzTEaoH5mc8/sVTnIx94T+J6H/zYp3Xu4sDS+XvuOqLPPf5hdba3Jqq3+hAC0xAjAtMQYIWOl/ZoTvfFang9vsEezV5N3RypvlBQ99GCaupqK9Rt/l+LwMx/hpWaAIFZKfL5fi8CM9/5VbJ7BGYl6ef73QjMfOdXye4RmJWkn+93IzDdy29hqF+z3/wvWhwbUfXOPap/2ztSa7IkMD/zu0+UCcGScHz6uWOpSUJTgVnq8Y2zl/Uj7/jupblL9S5cGjCSrNcDRGAaXicEpiFAR44P953W+PPLezT7+9Q5c66ss/I9mtHyHs22pWfO/frvaNfpf1DdwqQGWm/T/Lv+F+38zl5HJnOjDQSmGznksQsEZh5Tq3zPCMzKZ5DXDhCYeU2u8n0jMCufQV47QGDmNbnK943ArHwG13ewcOGsxv71B5bk5cqv2tsitfzq76XS6HoCc0USlv6z9KnJlU9U/pO3v1Wf/K0/ufYJyKHhMa18MnLf7m793qd+Yekr49d/AnNgeLTsE54rn+4s1f7lX/+i/uqrTy7N8Ssf+6lrgnKzwTbqebNzG/05AjMpueVzCExDgI4ev3L6kkafK0rH4+U9msfXdHq56bAWquq0e+Llsj8rfR297jf/2NHJKtMWArMy3H14KwLThxSznwGBmT1zX96IwPQlyeznQGBmz9yXNyIwfUky+zkQmHaZTz3xxW29YC5+TnPF59acqf/Ot6t6381brlXd2aP6t//wmuc3koHX//6KqPyh7zt67WvgQyNj+pmP/4Y+8tPv0cP33qnS848+9oUliVn6df0OzNWfwJyamlmSl3t2dS/VK9V69JNf0L/6lz+2pZ2ZX/7K1/XkszGfwNxy+pYfRGBaBuxI+emRcQ0/VdTcsVjNZ2LtGetTzeLcht2d+IH/Xfv++3/kSPeVbwOBWfkM8toBAjOvyVW2bwRmZfnn+e0IzDynV9neEZiV5Z/ntyMw85xeZXtHYNrlP/H5T2nmq39h9yXrVG/+wMe2JTBLn6L8td/5kh77xferJDBX/1Ce1eJzRUoefSDSfdGRGwrM9X7IT0ly3nJgz6afwrTxA4L4BKbhdURgGgLM8fHSHs2O//iY2mcvrjvFZHWrLndEy3s0I/UcLai6ribHEydvHYGZnF3oJxGYod+AZPMjMJNx45SEwOQWJCWAwExKjnMITO5AUgIIzKTktnYur5/AXE9gPvGXXyv7FOSKhNyKwLz+h/KskNvsa+QleVk699ij71/61GdavxCYhiQRmIYAc3783Kd/T7ee+LOyKearajVat1OdM+fLfn9R1TrfGml8X6TqOyN1PFRQU8/VPZq+/0Jg+p6wvfkQmPbY+lwZgelzunZnQ2Da5etzdQSmz+nanQ2BaZevz9URmG6l69IOzMc+/r5rX/E2/QTmyqc7t/qTxG3Jy1LaCEzDO4/ANASY8+Nz49MaevyTOtj/X5cmGa7bo/7v/Snte/fbtLRH89mrezTbLsbaNbH+Hs2R3ZF0a6TW+yK1HtmTcyLrt4/A9DLWTIZCYGaC2buXIDC9izSzgRCYmaH27kUITO8izWwgBGZmqL17EQLTvUgr/VPI1/va9soOzPe8621LX/u+0Q7M1TsrV+/ALBEvveP4qbP6wbc9vCYAG18bv/4lCEzDO4/ANAToyfHZ8SnNT0yrcWf7hhNND41r6FtFzb8Uq/ns+ns0R+r2aLA70tyhSE33ROq677AXhBCYXsRYkSEQmBXBnvuXIjBzH2HFBkBgVgx97l+MwMx9hBUbAIFZMfS5fzECM/cRbmuAknj8yQ89XnZm5SeFNzbWL/3+RgJx5VOR5y4OaKOfQl76qeQrsvOFl17VRj+F/PrzqwcoCdBf+tQfrJnr//rsx1P5KjkCc1tXZu3DCExDgEEfX1Rpj+Z0X1ENr8faOdSn5vmRMiJlezSj5T2atfnbo4nADPqiGw2PwDTCF+xhBGaw0RsPjsA0RhhsAQRmsNEbD47ANEYYbAEEZrDRBzs4AtMwegSmIUCOlxEYevE1jb9QVO3JPnX2x+qcOVf252/u0exVzZ0FtT9cUFO3+3s0EZhc9KQEEJhJyYV9DoEZdv4m0yMwTeiFfRaBGXb+JtMjME3ohX0WgRl2/iFOj8A0TB2BaQiQ4zckULZH80KsXZPr7dE8otIezcVbC2q7P1LrYff2aCIwuehJCSAwk5IL+xwCM+z8TaZHYJrQC/ssAjPs/E2mR2Ca0Av7LAIz7PxDnB6BaZg6AtMQIMe3RWBpj+bTseaPFTfco1n6QUJDPct7NO92Y48mAnNbMfPwdQQQmFyHJAQQmEmocaZEAIHJPUhKAIGZlBznEJjcgaQEEJhJyXEurwQQmIbJITANAXLciMDiwqL6nyxqOo6X92jGG+zR7NXUzZHqo4J6jhZUnfEeTQSmUcxBH0ZgBh1/4uERmInRBX8QgRn8FUgMAIGZGF3wBxGYwV+BxAAQmInRcTCnBBCYhsEhMA0Bcjx1AqU9mhPPx6o5FaurP1bHqj2aC6rWhdZejf5u2fcAACAASURBVO+LlvZodjwcqbG7NfU+ri+IwLSK1+viCEyv47U2HALTGlrvCyMwvY/Y2oAITGtovS+MwPQ+YmsDIjCtoaWwowQQmIbBIDANAXLcOoGx05c09mwsHS+q7UKfdk2eWPPOy00rezQjtT4Qqe3Q7lT7QmCmijOoYgjMoOJObVgEZmoogyuEwAwu8tQGRmCmhjK4QgjM4CJPbWAEZmooKZQTAghMw6AQmIYAOZ45gemhKxp6uqj5Y/HyHs1YNYtzZX1c3aPZq7lDkZruKajr3sNGfSIwjfAFfRiBGXT8iYdHYCZGF/xBBGbwVyAxAARmYnTBH0RgBn8FEgNAYCZGx8GcEkBgbhLcydPn9MGPfVrnLg5ce/Keu47oc49/WJ3trUJg5vTm0/Y1Ait7NGf6YtW/EWvn0AZ7NDt7NX1zpLrC9vdoIjC5cEkJIDCTkgv7HAIz7PxNpkdgmtAL+ywCM+z8TaZHYJrQC/ssAjPs/EOcHoG5BYH56OO/r8c+/j4dPrhvzdMIzBD/svF/5vI9mn3qmDlfNvTSHs225T2ad0TqeLhwwz2atQPDmq6rV01bs//wmDBVAgjMVHEGUwyBGUzUqQ+KwEwdaTAFEZjBRJ36oAjM1JEGUxCBGUzUDLpMAIGJwNzyXww9bQ0am5zV9OzCls/woB8Exk5f1NgzRelErLYL8Q33aOrWSC3LezTPfPHLOvjMH6phYWIJxGu736Zd/+Zf+wGFKTIhgMDMBLN3L0FgehdpZgMhMDND7d2LEJjeRZrZQAjMzFB79yIEpneRMtAmBBCYWxCY13+F/Pqvj5eO8glM/hoLkcDqPZp7R/tUrfkyFKO1O9U2d3kNnlfuf78OfOBHQ8TGzAkIIDATQOOIEJhcgqQEEJhJyXEOgckdSEoAgZmUHOcQmNyB0AggMLeZ+Gc+/4QuXBrQJz76XjU21mtiuvyHn2yzXK4eb6yr0ez8guYXFnPVN83aJ1Dao3n27/s0/kKfak+9qO6hPjXPj6774v6mw1r4nz6sfd/Vq+raavvN8YZcE2iqr9XUzLwWxX/v5DrIjJsv/ctgXW310t+zZuf41kDG+HP/uuaG2qD++S73gTkyQJWq1Fhfo8mZcP7dwBH0uW+juqpK9XXVS/+8wy8IbIdA6X84Kf0zz9RsOHen9PdofoVLAIG5zexLP9Tn137nS3rsF9+/9EN8hq/MbrNCfh8vfaKl9DfWuXlEQn5TzK7zk1/8cx3+h89u+MIF1Szt0Zw8EKn+rl71HO1VU3drdg3yplwQaNtRqyuTc1rAQeUiL1eabKivVlN9jaZnFjTJvxC6Eksu+ih9ArOtuU4j4+H8810ugslBk9XVWvr09+g4AjMHcTnVYklCNTfWaGyCu+NUMDloprbm6v9wUvpn5VB+dbTUhTIqc65DAIG5zWuxWmDyFfJtAuTxYAhMD41rx7/+MdUvTpXNfKb9ftXPjK27R/NS0xGN7u6Vbi2o9YFIrYd2B8OLQdcnwFfIuRlJCPAV8iTUOFMiwFfIuQdJCfAV8qTkOMdXyLkDSQnwFfKk5DiXVwIIzE2S+5uvPa3bDu2/9hPIS18hL/36yAfes/SfCMy8Xn36zoLAxf/vGdX93Z+qffwNTde2aPDO79WBD/7Y0qunhq5o+Kmi5o/Faj4Xa709msN1ezXUE2n2UKTmeyN13XMoi7Z5h0MEEJgOhZGjVhCYOQrLsVYRmI4FkqN2EJg5CsuxVhGYjgWSo3YQmDkKi1ZTIYDA3ATj088f009+6PFrT73z7Uev7b9EYKZyBykSAIGdHQ0aHptd2ke30a/FhQX1f6Oo6biohtdj7Szt0Vwo36M5Ud2m/s5IUzdHaogi9RwtqKqGPZo+XyEEps/p2psNgWmPre+VEZi+J2xvPgSmPba+V0Zg+p6wvfkQmPbYUtlNAghMw1z4BKYhQI4HQWArAnM9EIMvnNLk87FqT8Xq7I/VMXu+7LGVPZrj+yLV3FlQx0MFNbJH06s7hcD0Ks7MhkFgZobauxchML2LNLOBEJiZofbuRQhM7yLNbCAEZmaoeZEjBBCYhkEgMA0BcjwIAkkF5mo4Y6cuaey5WDoRq+1CvMEezVs1uieSjrBH04fLhcD0IcXsZ0BgZs/clzciMH1JMvs5EJjZM/fljQhMX5LMfg4EZvbMeWNlCSAwDfkjMA0BcjwIAmkJzNWwpgbHNPx0aY9mUTvO9WnPaKxqzZc9Nly/V4PdkeYPRWpij2bu7hsCM3eROdEwAtOJGHLZBAIzl7E50TQC04kYctkEAjOXsTnRNALTiRhoIkMCCExD2AhMQ4AcD4KALYG5Gt7i/IL6nyzt0YzVuLRHM1bT6j2aNW263NGr6aU9mgX1vLWgqmr2aLp6ERGYribjdl8ITLfzcbk7BKbL6bjdGwLT7Xxc7g6B6XI6bveGwHQ7H7pLnwAC05ApAtMQIMeDIJCVwFwPZmmP5sTzsepusEfzfFuvJlb2aD4SqbGzJYhc8jAkAjMPKbnXIwLTvUzy0hECMy9JudcnAtO9TPLSEQIzL0m51ycC071M6MguAQSmIV8EpiFAjgdBoJICczXgsVMXNfZsaY9mUW0X+7Rr8tU1GVxqWt6jeWuk1vsLaj20O4icXBwSgeliKu73hMB0PyNXO0RgupqM+30hMN3PyNUOEZiuJuN+XwhM9zOiw3QJIDANeSIwDQFyPAgCLgnM1cCnBpb3aL4ca8e5eOM9mj29mr8lUvO9BXXecyiI3FwYEoHpQgr56wGBmb/MXOkYgelKEvnrA4GZv8xc6RiB6UoS+esDgZm/zOjYjAAC04yfEJiGADkeBAGXBebqABbmFzRQtkezT00LY2WPTdS0qb+jV1PX9mhGqqquCiLLrIdEYGZN3I/3ITD9yLESUyAwK0Hdj3ciMP3IsRJTIDArQd2PdyIw/ciRKbZOAIG5dVbrPonANATI8SAI5ElgrhfI4PMnNfFCUbWnYnX196lj9kLZY/NVtbrQGmlif6SaOyJ1PlJQA3s0U7nbCMxUMAZXBIEZXOSpDYzATA1lcIUQmMFFntrACMzUUAZXCIEZXOTBD4zANLwCCExDgBwPgkDeBebqkN7coxmr/WKsnZvt0XygoNZb1u7RnJ+Z08A3Yi3Mzqrl9oNquXlnEPdhO0MiMLdDi2dXCCAwuQtJCSAwk5LjHAKTO5CUAAIzKTnOITC5A6ERQGAaJo7ANATI8SAI+CYwV4dWtkfzbKw9Y32q1kLZY8P1ezVY2qN5KFLzPQXNjU+o50/+T+2YH7r23CsP/bQO/NQ/DeJObHVIBOZWSfHc9QQQmNyHpAQQmEnJcQ6ByR1ISgCBmZQc5xCY3IHQCCAwDRNHYBoC5HgQBHwXmKtDXJgr7dGMNV0sqvH1WDuH1u7RnK+qU83ibNnRuap6TX32L1RdVxPEvdjKkAjMrVDimdUEEJjciaQEEJhJyXEOgckdSEoAgZmUHOcQmNyB0AggMA0TR2AaAuR4EARCE5jrhVraozm5vEezc509mitnThx8l6ofOKrOh9mjWWKCwAzivyJSHxKBmTrSYAoiMIOJOvVBEZipIw2mIAIzmKhTHxSBmTpSCjpOAIFpGBAC0xAgx4MggMBcG/PEz39APVOnbpj/pabbNLonkm4rqPWBSK0HdwVxX64fEoEZXOSpDIzATAVjkEUQmEHGnsrQCMxUMAZZBIEZZOypDI3ATAUjRXJEAIFpGBYC0xAgx4MggMBcG/OZz/+pbn/uC2V/cHHHHRo98IB2nIu1d6xPVav2aA7V79NQT3R1j+a9kTrvvsX7+4PA9D5iKwMiMK1gDaIoAjOImK0MicC0gjWIogjMIGK2MiQC0wpWijpMAIFpGA4C0xAgx4MggMBcP+azf/IV1b3yjKrnZzW951btef+Pq6ahbunhhbl59T9Z1Exc2qPZp53DsZoWxsoKTdS063JnpOmbIzVEkXqOFlRVXeXVnUJgehVnZsMgMDND7d2LEJjeRZrZQAjMzFB79yIEpneRZjYQAjMz1LzIEQIITMMgEJiGADkeBAEEZjoxD377pCZfjFV7KlZXf6z22QtlheeranWhtVcT+yPV3FnwYo8mAjOduxNaFQRmaImnNy8CMz2WoVVCYIaWeHrzIjDTYxlaJQRmaIkzLwLT8A4gMA0BcjwIAghMOzGPnbyo0ef6VHWiqPaLsXZOvrrmRW/u0YzU9kBBLTnbo4nAtHN3fK+KwPQ9YXvzITDtsfW9MgLT94TtzYfAtMfW98oITN8TZr7VBBCYhncCgWkIkONBEEBgZhPz1MCohp8uav5YUTvO9WnvWLzBHs1ezR8q5GKPJgIzm7vj21sQmL4lmt08CMzsWPv2JgSmb4lmNw8CMzvWvr0JgelbosyzGQEE5maENvlzBKYhQI4HQQCBWZmY39yjGavx9fgGezR7r+7R7C1o51sLktzZo4nArMzdyftbEZh5T7By/SMwK8c+729GYOY9wcr1j8CsHPu8vxmBmfcE6X+7BBCY2yW26nkEpiFAjgdBAIHpTsxLezRfWN6jObDZHs1oeY/mjooNgMCsGPpcvxiBmev4Kto8ArOi+HP9cgRmruOraPMIzIriz/XLEZi5jo/mExBAYCaAdv0RBKYhQI4HQQCB6W7MY69e0Ni3Y+lEvLxH8+SaZi8136bR3ZF0W/Z7NBGY7t4dlztDYLqcjtu9ITDdzsfl7hCYLqfjdm8ITLfzcbk7BKbL6dCbDQIITEOqCExDgBwPggACMz8xT/aPauRbpT2asXaci7V3rE9VWiwbYKh+n4Z6ejV/OFLzvQV19t5ibUAEpjW0XhdGYHodr9XhEJhW8XpdHIHpdbxWh0NgWsXrdXEEptfxMtw6BBCYhtcCgWkIkONBEEBg5jfmhdl59T9Z1ExxZY9mn5oWrpQNNF7Tof7OaHmPZrS8RzOdmRGY6XAMrQoCM7TE05sXgZkey9AqITBDSzy9eRGY6bEMrRICM7TEmReBaXgHEJiGADkeBAEEpl8xD377VU2+UFTtqVhdA31qn71YNuB8VZ0utEaaOBCp9s5IHY8U1NCebI8mAtOvu5PVNAjMrEj79x4Epn+ZZjURAjMr0v69B4HpX6ZZTYTAzIo073GFAALTMAkEpiFAjgdBAIHpd8xLezSfW96jeSnWzskN9mjuWd6jeX9BLQd3bQkKAnNLmHhoFQEEJlciKQEEZlJynENgcgeSEkBgJiXHOQQmdyA0AghMw8QRmIYAOR4EAQRmEDFfG3Lq8qiGnilq4YZ7NPdrqCda2qO5495IHb0H10A69+f/RXXD/ZptalHX279Djd2tYYFk2sQEEJiJ0QV/EIEZ/BVIDACBmRhd8AcRmMFfgcQAEJiJ0XEwpwQQmIbBITANAXI8CAIIzCBi3nDIhdm55T2aRTW+HmvXcJ8aN9mjWfvn/177R799reZYbbcmPvJZtR7aHTZMpt8SAQTmljDx0DoEEJhci6QEEJhJyXEOgckdSEoAgZmUHOfySgCBaZgcAtMQIMeDIIDADCLmbQ1Z2qM58UJRdaf61DUQr9mjuV6xV3r/uQ787P+8rffwcJgEEJhh5p7G1AjMNCiGWQOBGWbuaUyNwEyDYpg1EJhh5h7y1AhMw/QRmIYAOR4EAQRmEDEbDbmyR7PqRKxdZ59U69zlNfUmatp17uD3SrcV1PZApJabdxq9k8P+EkBg+put7ckQmLYJ+1sfgelvtrYnQ2DaJuxvfQSmv9ky2foEEJiGNwOBaQiQ40EQQGAGEXNqQ57/6yd15P/9pU3rDdXv19DOq3s0m++J1LnOHs1Ni/CAlwQQmF7GmslQCMxMMHv5EgSml7FmMhQCMxPMXr4EgellrAx1AwIITMPrgcA0BMjxIAggMIOIOdUhx37hZ7V74pVrNWeqGnX6bT+nxcF+Nb5R2qMZb7BHs1czN0eq7y1o51sLqfZEsfwQQGDmJyvXOkVgupZIfvpBYOYnK9c6RWC6lkh++kFg5icrOk2HAALTkCMC0xAgx4MggMAMIuZUh5ybmtHFJ/5WdcOXNNvUqta3fZfabt1b9o6rezRj1Z2K192jOVdVp4ttvZrYH6nmzoK6HolU396cap8Uc5MAAtPNXPLQFQIzDym52SMC081c8tAVAjMPKbnZIwLTzVzoyh4BBKYhWwSmIUCOB0EAgRlEzFaG3N3ZqP6Rac0vLG5af/TV87ryXKyqE0W1XezTzqlTa85cbL5dY3si6bZIbQ8W1HITezQ3BZvDBxCYOQzNkZYRmI4EkcM2EJg5DM2RlhGYjgSRwzYQmDkMjZaNCCAwjfBJCExDgBwPggACM4iYrQy5HYG5uoGpyyMa+lZRC8di7Tgfa99YLKlchF7do9l7dY/mvQV1RgetzEHRbAkgMLPl7dPbEJg+pZntLAjMbHn79DYEpk9pZjsLAjNb3ryt8gQQmIYZIDANAXI8CAIIzCBitjKkicBc3dD8zJwGnixqthirYZM9mtMHIzVGBfWwR9NKrraLIjBtE/a3PgLT32xtT4bAtE3Y3/oITH+ztT0ZAtM2Yeq7RgCBaZgIAtMQIMeDIIDADCJmK0OmKTDXa3DwuVc1+UKs2tdKezT71D57qeyx8j2akboeKbBH00rS6RZFYKbLM6RqCMyQ0k53VgRmujxDqobADCntdGdFYKbLk2ruE0BgGmaEwDQEyPEgCCAwg4jZypC2Bebqpkt7NMeei1V9Ilb7xVg9m+zRbH+woB3s0bSSvUlRBKYJvbDPIjDDzt9kegSmCb2wzyIww87fZHoEpgk9zuaRAALTMDUEpiFAjgdBAIEZRMxWhsxaYK4eYmmP5tNFLbwcq+V8rL1jfWvmZI+mleiNiiIwjfAFfRiBGXT8RsMjMI3wBX0YgRl0/EbDIzCN8HE4hwQQmIahITANAXI8CAIIzCBitjJkpQXm6qFW9mjOFGM1vRFr53CfGhfGyx4br+lUf1ek6ZsjNfZG6jl6lxU2FN2YAAKT25GUAAIzKTnOITC5A0kJIDCTkuMcApM7EBoBBKZh4ghMQ4AcD4IAAjOImK0M6ZrAXG/IwWdPaPLF4g32aNbrYluk8f2Rau+K1PUwezStXJbriiIwbRP2tz4C099sbU+GwLRN2N/6CEx/s7U9GQLTNmHqu0YAgWmYCALTECDHgyCAwAwiZitD5kFgrh589MTyHs1XN9uj2SvdVhB7NNO/OgjM9JmGUhGBGUrS6c+JwEyfaSgVEZihJJ3+nAjM9JlS0W0CCEzDfBCYhgA5HgQBBGYQMVsZMo8CczWIyUsjGvlWUfOlPZrnYu29snaP5mD9AQ3vjDR/OFLzvZE6o5ut8AylKAIzlKTTnxOBmT7TUCoiMENJOv05EZjpMw2lIgIzlKSZc4UAAtPwLiAwDQFyPAgCCMwgYrYypA8CczWY+elZDXyzqJm4qMYzsXYl2KN59s++qupXXlTVwrzmb75D+3/iXVb457UoAjOvyVW+bwRm5TPIawcIzLwmV/m+EZiVzyCvHSAw85ocfSclgMBMSm75HALTECDHgyCAwAwiZitD+igw1wM18OwJTb0Yq/ZUrO6BWG1zl8oem6uq14W2Xk0eiFQzdEGHz/1d2Z+/etM7tPfRn7eSQR6LIjDzmJobPSMw3cghj10gMPOYmhs9IzDdyCGPXSAw85gaPZsQQGCa0JOEwDQEyPEgCCAwg4jZypChCMzV8EaPn9fYt2NVn4jVfilWz9SpTfmOffY/qaa+dtPnQngAgRlCynZmRGDa4RpCVQRmCCnbmRGBaYdrCFURmCGkzIzXE0BgGt4HBKYhQI4HQQCBGUTMVoYMVWCuhjl5aVjD3ypq4eWijrzyZ6rW/Brew3X7NLjrbvZoSkJgWvnLMYiiCMwgYrYyJALTCtYgiiIwg4jZypAITCtYKeowAQSmYTgITEOAHA+CAAIziJitDInAXIt19KM/pz3jL5X9waKqVKXFst+7UtOp/q5ezRyM1NhbUM9b7rKSkYtFEZguppKPnhCY+cjJxS4RmC6mko+eEJj5yMnFLhGYLqZCTzYJIDAN6SIwDQFyPAgCCMwgYrYyJAJzLdbzf/F1HflPnyj7g+MP/4wa77tbky/GqtvCHs3auwrqeiRSXWuTldwqXRSBWekE8vt+BGZ+s6t05wjMSieQ3/cjMPObXaU7R2BWOgHenzUBBKYhcQSmIUCOB0EAgRlEzFaGRGCuj3X8jcsafe4lLS4saMcdR9R+101rHhw9fk5XnotV9WpR7Zf61DP12ppnLjbfobG9kXRbpPYHC9pxoMdKjlkXRWBmTdyf9yEw/cky60kQmFkT9+d9CEx/ssx6EgRm1sR5X6UJIDANE0BgGgLkeBAEEJhBxGxlSARmelgnLy7v0XwlVsu5WHuvxGuKDzYc0PDOSPOHerXjvoI6Cjen10CGlRCYGcL27FUITM8CzXAcBGaGsD17FQLTs0AzHAeBmSFsXuUEAQSmYQwITEOAHA+CAAIziJitDInAtIJ1qejc9KwGnyxqphir6Y1Yu0b61LAwUfbC0h7Nga5eTedsjyYC09698b0yAtP3hO3Nh8C0x9b3yghM3xO2Nx8C0x5bKrtJAIFpmAsC0xAgx4MggMAMImYrQyIwrWDdsOjAs8c1+UJRda/F6h7oU9vc5bJnZ6sadLEt0uSBSLV3Rep6pODkHk0EZrb3xqe3ITB9SjPbWRCY2fL26W0ITJ/SzHYWBGa2vHlb5QkgMA0zQGAaAuR4EAQQmEHEbGVIBKYVrFsuOnL8nMaX9mjGar8Ur79Hc8cdGtvj1h5NBOaWI+bBVQQQmFyJpAQQmEnJcQ6ByR1ISgCBmZQc5/JKAIFpmBwC0xAgx4MggMAMImYrQyIwrWBNXPTaHs2XY7Wcv9EezV7NH46u7tG8K/s9mgjMxBEHfxCBGfwVSAwAgZkYXfAHEZjBX4HEABCYidFxMKcEEJiGwSEwDQFyPAgCCMwgYrYyJALTCtbUis5NzWrgm7HmikU1brhHs0v9XZFmD0Zq6I3U85Y7U3v/RoUQmNYRe/sCBKa30VofDIFpHbG3L0Bgehut9cEQmNYR8wLHCCAwDQNBYBoC5HgQBBCYQcRsZUgEphWsVotudY/mxIFIdZb2aCIwrUbsdXEEptfxWh0OgWkVr9fFEZhex2t1OASmVbwUd5AAAtMwFASmIUCOB0EAgRlEzFaGRGBawZpp0dIezSvPxaq+wR7NCzvu1JU9kapuL6j1wUgt+7uNekRgGuEL+jACM+j4jYZHYBrhC/owAjPo+I2GR2Aa4eNwDgkgMA1DQ2AaAuR4EAQQmEHEbGVIBKYVrBUtenWPZqyFl4s32KN5k4Z2RlpY2qMZqeOum7bVMwJzW7h4+DoCCEyuQ1ICCMyk5DiHwOQOJCWAwExKjnN5JYDANEwOgWkIkONBEEBgBhGzlSERmFawOlV0bnJGA98sarZYVNOZPu0aidWwMFHW45Waq3s0Zw5Garw7Us8jN96jicB0KuJcNYPAzFVcTjWLwHQqjlw1g8DMVVxONYvAdCoOmsmAAALTEDIC0xAgx4MggMAMImYrQyIwrWB1vujAM8c19WKsutdidQ3Eapu7XNbzbFWDLrb3amJ/aY9mQV2PFFTX2rT0zIW/flJ1//BXapq4rOnGTk0+8oPa9+63OT8zDbpBAIHpRg557AKBmcfU3OgZgelGDnnsAoGZx9To2YQAAtOEniQEpiFAjgdBAIEZRMxWhkRgWsGau6JX92j2qfrVotovxeqZem3NDKU9mhPtN+vwub9d82enf+Kz2vnWQu7mpuHsCSAws2fuyxsRmL4kmf0cCMzsmfvyRgSmL0kyx1YJIDC3SmqD5xCYhgA5HgQBBGYQMVsZEoFpBWvui05cHNLIt4rLezT7tPdK8YYznTj0bu372M/mfm4GsE8AgWmfsa9vQGD6mqz9uRCY9hn7+gYEpq/JMtdGBBCYhncDgWkIkONBEEBgBhGzlSERmFawele0tEdz8JtF1fztn+qmoafXne9KbZf6O3s1c0ukxt7Cpns0vYPEQFsigMDcEiYeWocAApNrkZQAAjMpOc4hMLkDoRFAYBomjsA0BMjxIAggMIOI2cqQCEwrWL0teuHvvqXDX/7FNfNN1rSqaX6s7PdX9mhOHohUe1d0dY9mS6O3bBhsawQQmFvjxFNrCSAwuRVJCSAwk5LjHAKTOxAaAQSmYeIITEOAHA+CAAIziJitDInAtILV66Ln/u1v6dbX/uLajCf3fb/2/NLHNPLKWV35dlHVr/Yt79E8vYZDaY/m2J5I1bdHanuwoB37u71mxXBrCSAwuRVJCSAwk5LjHAKTO5CUAAIzKTnO5ZUAAtMwOQSmIUCOB0EAgRlEzFaGRGBawep/0eExLQ4Mq6q9TeppX3feiQtDGnmmtEczVsv5eN09moMNN2l4Z6T5w73acV9BHXfd5D+7wCdEYAZ+AQzGR2AawAv8KAIz8AtgMD4C0wAeR3NJAIFpGBsC0xAgx4MggMAMImYrQyIwrWD1vmhLU63amut0ZXJOoxOzW5p3ZY/mTDFW05lYu0b61LAwWXb2Sm23+rsizRws7dGM1PPIHVuqzUP5IYDAzE9WrnWKwHQtkfz0g8DMT1audYrAdC0R+rFNAIFpSBiBaQiQ40EQQGAGEbOVIRGYVrB6XzSJwFwPysC3XtHki0XVvxare7BPrXP9ZY/NVjXqYnuka3s031JQ3Q72aOb5giEw85xeZXtHYFaWf57fjsDMc3qV7R2BWVn+vD17AghMQ+YITEOAHA+CAAIziJitDInAtILV+6JpCczVoEZefnOPZselWN3TG+zR3Bup6vZI7Q+wRzNvlw2BmbfE3OkXgelOFnnrBIGZt8Tc6ReB6U4WdJINAQSmIWcEpiFAjgdBAIEZRMxWhkRgWsHqfVFbAnM1uInzy3s0X4nVej7WurmrTgAAIABJREFUnivFNWwHGm5e2qO5cCRSy72R2u864D3/PA+IwMxzepXtHYFZWf55fjsCM8/pVbZ3BGZl+fP27AkgMA2ZIzANAXI8CAIIzCBitjIkAtMKVu+LZiUwV4Ocm5zW4DeLmi0W1Xgm1u7hPtUvlu/RHKvt1sDKHs27I/U8zB5Nly4kAtOlNPLVCwIzX3m51C0C06U08tULAjNfedGtOQEEpiFDBKYhQI4HQQCBGUTMVoZEYFrB6n3RSgnM9cC+uUezT92D8Zo9mjNVjbp03R7N7rcUVMsezYrdUQRmxdDn/sUIzNxHWLEBEJgVQ5/7FyMwcx8hA2yTAAJzm8BWP47ANATI8SAIIDCDiNnKkAhMK1i9L+qSwFwN++oezVjVr8baeI/mXbqyN5JuL6j9wUg79nV5n5krAyIwXUkif30gMPOXmSsdIzBdSSJ/fSAw85cZHZsRQGCa8RMC0xAgx4MggMAMImYrQyIwrWD1vqjLAnM1/Kt7NGMtvFxU64Ub7NHcFWnhcKSW+yK138keTVuXGIFpi6z/dRGY/mdsa0IEpi2y/tdFYPqfMROWE0BgbuFGfPkrX9cvfeoPlp5859uP6hMffa8aG+uX/n8E5hYA8kjwBBCYwV+BxAAQmInRBX0wTwJzdVBzE9MaeKqouWK8vEcz3mCPZq9mD0ZquLvAHs0UbzsCM0WYgZVCYAYWeIrjIjBThBlYKQRmYIEzrhCYm1yCp58/ps/87hP63OMfVmd7qz7z+SeWTnzkA+9BYPIXEAS2SACBuUVQPLaGAAKTS5GEQJ4F5nrzXt2jGav+tXjDPZoX23s1eSBSXaGg7kci1e5oSIIu+DMIzOCvQGIACMzE6II/iMAM/gokBoDATIyOgzklgMDcJLiSsLzlwB79yDu+e+nJ1UKTT2Dm9ObTdqYEEJiZ4vbqZQhMr+LMbBjfBOZqcCMvn9GVbxeX92j2qXv69TVsL+y4ukez6vZIbQ8VtGNvl0aOn9Xcv/9t3TT09NLzb3Q+rNp/8bNqv21/Ztm4/iIEpusJudsfAtPdbFzvDIHpekLu9ofAdDcbOrNDAIF5A65TUzP65V//oo4+EF0TmCdPn9Ojj/++Hvv4+3T44D6+Qm7nXlLVMwIITM8CzXAcBGaGsD16le8Cc3VUE+cHNfKtohZeidV6Ptae8ZfWpDnQcLPq5ifUNtdf9mclidn92GMepW82CgLTjF/IpxGYIadvNjsC04xfyKcRmCGnH+bsCMwtCMz3vOttevjeO5eeXC0ww7w2TA0BCEAAAhCAgKsEZq5M642/f0FXnn9Rtadf1M6hvjV7NK/vfeznPq+bvqvg6jj0BQEIQAACEIAABCAAAXZg3ugObOUTmNwhCEAAAhCAAAQg4DqBN/5rUa2f/cCGbc5UNelyZ6/mDt6tlnvv1k3fc4/qW9ij6Xqu9AcBCEAAAhCAAARCIcAnMDdJmh2YbwLqaWvQ2OSspmcXQvnrgzlTIsBXyFMCGWAZvkIeYOgpjBzaV8i3imzg0Uev7b9cOTNa26PZmuYN92iO7Y1UfXuk9ocKat7btdVX5fY5vkKe2+gq3jhfIa94BLltgK+Q5za6ijfOV8grHgENZEwAgbkJcH4KOQIz478mvXwdAtPLWDMZCoGZCWbvXoLAXD/SG/0Qn/Hzgxrdwh7N4V29WjgSqeW+gtrvOODd3UFgehdpZgMhMDND7d2LEJjeRZrZQAjMzFDzIkcIIDC3EMSXv/J1/dKn/mDpyXe+/ag+8dH3qrGxfun/56eQbwEgjwRPAIEZ/BVIDACBmRhd0AcRmObxz41Pa+CpWLPFoprOxNo9UtqjOVVWeKy2RwNdkWZuidR0d6Tuh243f3GFKyAwKxxAjl+PwMxxeBVuHYFZ4QBy/HoEZo7Do/VEBBCYibC9eQiBaQiQ40EQQGAGEbOVIRGYVrB6XxSBaSfi/qdf1vSLRdWdjtU92KfWuYGyF5X2aF7siDR1IFLtXZG631JQbXO+9mgiMO3cnRCqIjBDSNnOjAhMO1xDqIrADCFlZryeAALT8D4gMA0BcjwIAgjMIGK2MiQC0wpW74siMLOJeOTYGV35dqzqk7E6LsU32KPZq+rbC7nYo4nAzObu+PgWBKaPqWYzEwIzG84+vgWB6WOqzHQjAghMw/uBwDQEyPEgCCAwg4jZypAITCtYvS+KwKxMxOPnBjXyTFF6JVbL+Vh7xl9a08hAw0EN74qW92hGar9jf2Wa3eCtCEyn4shVMwjMXMXlVLMITKfiyFUzCMxcxUWzKRBAYBpCRGAaAuR4EAQQmEHEbGVIBKYVrN4XRWC6EfHc+JQGvlnU7EtFNZ+JtSsHezQRmG7cnTx2gcDMY2pu9IzAdCOHPHaBwMxjavRsQgCBaUKPH+JjSI/joRBAYIaSdPpzIjDTZxpCRQSmuylf3aMZL+/RjDfYo9m7tEezrlBQV2mPZlN2ezQRmO7eHdc7Q2C6npC7/SEw3c3G9c4QmK4nRH9pE0BgGhLlE5iGADkeBAEEZhAxWxkSgWkFq/dFEZj5iXhLezRbChrbG6n69kjtDxbUvLfT2oAITGtovS+MwPQ+YmsDIjCtofW+MALT+4gZcBUBBKbhlUBgGgLkeBAEEJhBxGxlSASmFazeF0Vg5jfi8bMDGnm2tEezqJbzfdozfmzNMDb3aCIw83t3Kt05ArPSCeT3/QjM/GZX6c4RmJVOgPdnTQCBaUgcgWkIkONBEEBgBhGzlSERmFawel8UgelPxLPjUxr8ZlFzL8VqOhNr90isusWpsgHHans00NWrmVsiNd1dUPdDtycGgMBMjC74gwjM4K9AYgAIzMTogj+IwAz+CgQHAIFpGDkC0xAgx4MggMAMImYrQyIwrWD1vigC0++I+596WVN9sepPx+oZjNUyN1A28HR1ky6192ryQKT6pT2akWqb6rcEBYG5JUw8tA4BBCbXIikBBGZScpxDYHIHQiOAwDRMHIFpCJDjQRBAYAYRs5UhEZhWsHpfFIHpfcRlAw6/9IbGny+q+tVYHZf71D39xhoA51sKGt8bqaq0R/Ohgpr3rL9Hc/xsv5onJzXZ0rLhM2HRZdqtEkBgbpUUz60mgMDkTiQlgMBMSo5zeSWAwDRMDoFpCJDjQRBAYAYRs5UhEZhWsHpfFIHpfcQ3HHBpj+YzRS0ej9V6Pl53j2Z/40GN7Iy0cKRXLfcV1H7Hfl34lU/p8Lm/u1b7xC0/rH3/2/8aNkym3zIBBOaWUfHgKgIITK5EUgIIzKTkOJdXAghMw+QQmIYAOR4EAQRmEDFbGRKBaQWr90URmN5HvK0BZ69MafCp6/do9qlucbqsxmRNq5rmx9bUPfkjn9Se739oW+/j4TAJIDDDzD2NqRGYaVAMswYCM8zcQ54agWmYPgLTECDHgyCAwAwiZitDIjCtYPW+KALT+4iNB+x/6pim+oqqfy1Wz1CfWuYG1635RufDmv+BH1XXWwpb3qNp3BwFckkAgZnL2JxoGoHpRAy5bAKBmcvYaNqAAALTAF7pKALTECDHgyCAwAwiZitDIjCtYPW+KALT+4hTH/Dcp35bt5768xvWLe3RvLI3UvUdy3s0d6+/RzP15iiYCwIIzFzE5GSTCEwnY8lFUwjMXMREkykSQGAawkRgGgLkeBAEEJhBxGxlSASmFazeF0Vgeh9x6gNe/kZRB//oQ2vqntz3A2oeeX3jPZq7erVwJFLL/QW137Y/9b4omB8CCMz8ZOVapwhM1xLJTz8IzPxkRafpEEBgGnJEYBoC5HgQBBCYQcRsZUgEphWs3hdFYHofsZUBz/3519Twzb9R0/SQJpp2au6736k9//jo0rtmx0p7NGPNHSuq6Uys3SNr92iO1u7UYHek2YORGu+J1P3gbVb6pKibBBCYbuaSh64QmHlIyc0eEZhu5kJX9gggMA3ZIjANAXI8CAIIzCBitjIkAtMKVu+LIjC9j9jagFVV0p7OJp0fnNz0HWV7NAf71DJfvkdzurpZl9ojTR6IVFeI1M0ezU2Z5vkBBGae06ts7wjMyvLP89sRmHlOj96TEEBgJqF23RkEpiFAjgdBAIEZRMxWhkRgWsHqfVEEpvcRWxtwOwJzdRPDL72h8W/HqjkZq+NyrK7pN9b0eb4lWt6jWVDHQ5GadndYm4XC2RJAYGbL26e3ITB9SjPbWRCY2fLmbZUngMA0zACBaQiQ40EQQGAGEbOVIRGYVrB6XxSB6X3E1gY0EZirmxo/O6DRZ2ItvlJUy4V4gz2at2hkV7S8RzNS+237rM1GYbsEEJh2+fpcHYHpc7p2Z0Ng2uVLdfcIIDANM0FgGgLkeBAEEJhBxGxlSASmFazeF0Vgeh+xtQHTFJirm5wdm9TgU0XNvlRU85k+7R6NVbc4XfZYaY/mQGmP5i2Rmkp7NB9gj6a1sFMujMBMGWhA5RCYAYWd8qgIzJSBUs55AghMw4gQmIYAOR4EAQRmEDFbGRKBaQWr90URmN5HbG1AmwJzvab7v3lMU32x6k/H6hmMN9ij2avJmyLV3VVQ99FItY111uancHICCMzk7EI/icAM/QYknx+BmZwdJ/NJAIFpmBsC0xAgx4MggMAMImYrQyIwrWD1vigC0/uIrQ2YtcBcPcjKHs3qk7E6N92jGanjoQJ7NK3dhu0VRmBujxdPv0kAgcltSEoAgZmUHOfySgCBaZgcAtMQIMeDIIDADCJmK0MiMK1g9b4oAtP7iK0NWGmBuXqw8TP9Gn22uLRHs/VCn3aPv7xm9v7Gq3s0F49E2nE/ezStXY5NCiMwK0U+/+9FYOY/w0pNgMCsFHneWykCCExD8ghMQ4AcD4IAAjOImK0MicC0gtX7oghM7yO2NqBrAnP1oG/u0YzVfCa+wR7N3uU9mgX2aFq7LeWFEZgZgfbwNQhMD0PNaCQEZkageY0zBBCYhlEgMA0BcjwIAgjMIGK2MiQC0wpW74siML2P2NqArgvM9QYv7dGcXt6j2T3Yp5b5obLHpqubdam9V1OlPZqFSF1vKbBH08INQmBagBpISQRmIEFbGBOBaQEqJZ0mgMA0jAeBaQiQ40EQQGAGEbOVIRGYVrB6XxSB6X3E1gbMo8BcDWO4+LrGny+q5mSfOpb2aJ5Zw+t8S6QreyNV38EezbQuEwIzLZLh1UFghpd5WhMjMNMiSZ28EEBgGiaFwDQEyPEgCCAwg4jZypAITCtYvS+KwPQ+YmsD+iAwV8Mp7dEceaYoHY/Vej7W7okb79FsuT9S22371jAeeekNjb/8qqqqq9V2/13acdNOaznksTACM4+pudEzAtONHPLYBQIzj6nRswkBBKYJPUkITEOAHA+CAAIziJitDInAtILV+6IITO8jtjagjwJzNayVPZpzL8VqWtqj2ae6xZmyx0Zrd2mgO1reoxlp6tsv6ranP1f2zKs/9Mva+8PfbS2LvBVGYOYtMXf6RWC6k0XeOkFg5i0x+jUlgMA0JIjANATI8SAIIDCDiNnKkAhMK1i9L4rA9D5iawOGIDDXg9f/zZc01VdUw+lY6+3RXFSVqrRYdvTCjrvU9uu/aS2LvBVGYOYtMXf6RWC6k0XeOkFg5i0x+jUlgMA0JIjANATI8SAIIDCDiNnKkAhMK1i9L4rA9D5iawOGKjBXA13ao/ntq3s0uy69qI7Zc2uYL6hGr97+T6/u0XywoKbdHdZyyUNhBGYeUnKzRwSmm7nkoSsEZh5Sosc0CSAwDWkiMA0BcjwIAgjMIGK2MiQC0wpW74siML2P2NqACMy1aOdn5tT6oR/alHl/4yGN7Iq0cGtBrff1qu22vZue8ekBBKZPaWY7CwIzW94+vQ2B6VOazLIVAgjMrVC6wTMITEOAHA+CAAIziJitDInAtILV+6IITO8jtjYgAnN9tOcf+3c68sZXyv7w5L7v13znnqU9mntG+1S70R7NQ5Ga7o7U/cCt1nJzoTAC04UU8tkDAjOfubnQNQLThRToIUsCCExD2ghMQ4AcD4IAAjOImK0MicC0gtX7oghM7yO2NiACc2O0Z//oL1Xz+starK7Rwu13a///8Payh5f2aL4Yq/71WDsHY+2YHyr786nqHbrUHmnqpl7VRwV1v6WgmoY6a1lmXRiBmTVxf96HwPQny6wnQWBmTZz3VZoAAtMwAQSmIUCOB0EAgRlEzFaGRGBawep9UQSm9xFbGxCBmR7aofh1TTwfq+ZkrI7Lsbpmzqwpfr6lV1f2Raq5o6D2hyI17WpPr4GMKyEwMwbu0esQmB6FmfEoCMyMgfO6ihNAYBpGgMA0BMjxIAggMIOI2cqQCEwrWL0visD0PmJrAyIwraHV+BuXNfJMUTpeVOuFWLsnXl7zsqU9mrsjLRyJ1Hp/pLZb87NHE4Fp7+74XhmB6XvC9uZDYNpjS2U3CSAwDXNBYBoC5HgQBBCYQcRsZUgEphWs3hdFYHofsbUBEZjW0K4pPDMyocGni5o/Fi/v0YzX7tGs26WBrl7NLe3RLKjL4T2aCMzs7o5vb0Jg+pZodvMgMLNjzZvcIIDANMwBgWkIkONBEEBgBhGzlSERmFawel8Ugel9xNYGRGBaQ7ulwv1PvqSpvlgNr8fq2WiPZkevpm6KVF8oqPtopJr62i3Vtv0QAtM2YX/rIzD9zdb2ZAhM24Sp7xoBBKZhIghMQ4AcD4IAAjOImK0MicC0gtX7oghM7yO2NiAC0xraRIWH4tOaeL64tEez83KfOmfOrqnz5h7NSB0PF9S4szJ7NBGYiSLmkCQEJtcgKQEEZlJynMsrAQSmYXIITEOAHA+CAAIziJitDInAtILV+6IITO8jtjYgAtMa2lQKv7lHM17eo/nKmrqlPZrDuyMtlvZoPhCp7Ug2ezQRmKlEHGQRBGaQsacyNAIzFYwUyREBBKZhWAhMQ4AcD4IAAjOImK0MicC0gtX7oghM7yO2NiAC0xpaK4WX9mg+VdTcsVg7zsbaPbp2j+ZI3S4Ndvdq7ha7ezQRmFYiDqIoAjOImK0MicC0gpWiDhNAYBqGg8A0BMjxIAggMIOI2cqQCEwrWL0visD0PmJrAyIwraHNrHD/N4qaiovLezT7tGN+uOzdU9UtutQRLe/RjNR9tJDKHk0EZmYRe/ciBKZ3kWY2EAIzM9S8yBECCEzDIBCYhgA5HgQBBGYQMVsZEoFpBav3RRGY3kdsbUAEpjW0FSu8+R7NKp1rjTS+N1L1HZE6E+7RRGBWLOLcvxiBmfsIKzYAArNi6HlxhQggMA3BIzANAXI8CAIIzCBitjIkAtMKVu+LIjC9j9jagAhMa2idKXzljcsafaYoHd94j+blxkMa3d2rhVsLar1/a3s0EZjORJy7RhCYuYvMmYYRmM5EQSMZEUBgGoJGYBoC5HgQBBCYQcRsZUgEphWs3hdFYHofsbUBEZjW0Dpb+OoezVjzx4pqXtqj2afaxdmyfkfqdmuwO9LsoUjNd0fquv9I2Z+Pnjivsa/9g+omxzTbsUu73/MDqm2sd3ZmGnOLAALTrTzy1A0CM09p0WsaBBCYhhQRmIYAOR4EAQRmEDFbGRKBaQWr90URmN5HbG1ABKY1tLkqfPkbRc30FVX/eqyeoY33aE7fFEldPTr4td9U/eLUtRkvNt+u1k//dq5mptnKEUBgVo593t+MwMx7gvS/XQIIzO0SW/U8AtMQIMeDIIDADCJmK0MiMK1g9b4oAtP7iK0NiMC0hjbXhYf6TmvihVg1J2N1Xo7VOXN203le/e9+RXv/8dFNn+MBCCAwuQNJCSAwk5LjXF4JIDANk0NgGgLkeBAEEJhBxGxlSASmFazeF0Vgeh+xtQERmNbQelX4yuuXNfpsLB0vat/p/6zm+ZE1843V7tSl/Ue1eGu0tEez9cgerxgwTHoEEJjpsQytEgIztMSZF4FpeAcQmIYAOR4EAQRmEDFbGRKBaQWr90URmN5HbG1ABKY1tN4WPvPbf6zb+/5w0/nK9mjeE6nrvvI9mpsW4AFvCSAwvY3W+mAITOuIeYFjBBCYhoEgMA0BcjwIAgjMIGK2MiQC0wpW74siML2P2NqACExraL0tPHbqopo/8yG1zg1cm/Fs232ae/e/0HRfrIalPZqxdswPlzGYqm7RpY5eTd0UqT4qqOdoQdV1td5yYrCNCSAwuR1JCSAwk5LjXF4JIDANk0NgGgLkeBAEEJhBxGxlSASmFazeF0Vgeh+xtQERmNbQel14amBMg1/9b6qbvKLZjh7te/c/WjPvcN9pjT8fq+bU+ns0F1Wl8629Gt8XqfqOSJ0PFdS4s81rbgx3lQACk5uQlAACMyk5zuWVAALTMDkEpiFAjgdBAIEZRMxWhkRgWsHqfVEEpvcRWxsQgWkNrfeFa6qr1NPeoItDb/408hsNfeX0JY0+V1zao9l2oU+7Jo6vefxy42GN7o7Yo+n57UFgeh6wxfEQmBbhUtpJAghMw1gQmIYAOR4EAQRmEDFbGRKBaQWr90URmN5HbG1ABKY1tN4X3q7AXA1kemRcw08VNXcsVvOZWHvGYtUszpY9dnWPZq9mD0VqvqfAHk1PbhUC05MgKzAGArMC0HllRQkgMA3xIzANAXI8CAIIzCBitjIkAtMKVu+LIjC9j9jagAhMa2i9L2wqMNcDdPkbxRvu0ZysbtHl0h7NmyPVF6LlPZo13rP2bUAEpm+JZjcPAjM71rzJDQIITMMcEJiGADkeBAEEZhAxWxkSgWkFq/dFEZjeR2xtQASmNbTeF7YhMFdDG+p7TRPPF1VzMlZnf586Z86VPVK2R/POSB0PFdTUwx5N1y8fAtP1hNztD4HpbjZ0ZocAAtOQKwLTECDHgyCAwAwiZitDIjCtYPW+KALT+4itDYjAtIbW+8JZCMzVEJf2aD5blE7EarsQr79Hs+mwRnZH0pFIrfdHaj2yx/ss8jYgAjNvibnTLwLTnSzoJBsCCExDzghMQ4AcD4IAAjOImK0MicC0gtX7oghM7yO2NiAC0xpa7wtXQmCuhjo9NK6hbxU1/1Ks5rOlPZp9qlmcK3tsZY/m3KFITfdE6rrvsPfZuD4gAtP1hNztD4HpbjZ0ZocAAtOQKwLTECDHgyCAwAwiZitDIjCtYPW+KALT+4itDYjAtIbW+8IuCMy1kBd1dY9mUQ2vx9o51Kfm+ZGyxyarW3W5I7q6RzNa3qNZyx7NLC8sAjNL2n69C4HpV55MszkBBObmjG74BALTECDHgyCAwAwiZitDIjCtYPW+KALT+4itDYjAtIbW+8JuCsy12IdefE3jLxRVu+EezWqdb400vi9SzZ2R2h8uqKmbPZo2LzAC0yZdv2sjMP3Ol+nWEkBgGt4KBKYhQI4HQQCBGUTMVoZEYFrB6n1RBKb3EVsbEIFpDa33hfMiMFcHcW2P5vFYbRdvtEezV7q1oNb7e9V6eLf3eWY5IAIzS9p+vQuB6VeeTLM5AQTm5oxu+AQC0xAgx4MggMAMImYrQyIwrWD1vigC0/uIrQ2IwLSG1vvCeRWYq4OZHrqioaeLmj9WvMEezT0a7Ik0dwt7NNO42AjMNCiGWQOBGWbuIU+NwDRMH4FpCJDjQRBAYAYRs5UhEZhWsHpfFIHpfcTWBkRgWkPrfWFfBObqoBYXFtX/ZFHTcbI9mvPTs7rwhf+ohgsntFBTp9nbH9T+f/YO7+/DdgZEYG6HFs9eTwCByX0IjQAC0zBxBKYhQI4HQQCBGUTMVoZEYFrB6n1RBKb3EVsbEIFpDa33hX0VmOsFV9qjOfF8rJpTsTr7Y3XOnCt7bFGlPZq9S3s02848q93jL5f9+Sv3v18HPvCj3t+JrQ6IwNwqKZ5bTQCByZ0IjQAC0zBxBKYhQI4HQQCBGUTMVoZEYFrB6n1RBKb3EVsbEIFpDa33hUMSmKvDHDt9SWPPxtLxotouxNo1efyGefc3HlLzv/u893diqwMiMLdKiucQmNK+7iYuQsAEEJiG4SMwDQFyPAgCCMwgYrYyJALTClbviyIwvY/Y2oAITGtovS8cssBcHe7KHs2FZ5/Uraf/ct3sh+v2aKi0R/NQr5ruKajr3sPe35GNBkRgBhu98eB8AtMYIQVyRgCBaRgYAtMQIMeDIIDADCJmK0MiMK1g9b4oAtP7iK0NiMC0htb7wgjMtREvzM6r8UM/rNrFmbI/nK+qU83ibNnvTVa36nJnr6ZvjlRXKKjnaKTq2mrv701pQARmEDFbGRKBaQUrRR0mgMA0DAeBaQiQ40EQQGAGEbOVIRGYVrB6XxSB6X3E1gZEYFpD631hBOb6EZ/5g/9Ht3/rd6/94XhNp/r/2f+h2pZmTTxf3HCP5oKqdaG0R3N/pJo7InU8XFBjd6uX9wiB6WWsmQyFwMwEMy9xiAAC0zAMBKYhQI4HQQCBGUTMVoZEYFrB6n1RBKb3EVsbEIFpDa33hRGYG0d85fXLuvLKaVXX1an7rZFq6mvXPDz22kWNPVeUjsfLezRPrHnmctMRjeyOpFsjtTwQqe3Qbi/uFQLTixgrMgQCsyLYeWkFCSAwDeEjMA0BcjwIAgjMIGK2MiQC0wpW74siML2P2NqACExraL0vjMBMN+KVPZrzx2I1n421ZyxWzeJc2UtKezQHe3o1dyhSc473aCIw0707IVVDYIaUNrOWCCAwDe8BAtMQIMeDIIDADCJmK0MiMK1g9b4oAtP7iK0NiMC0htb7wghMuxEvLiyq/xuxpuOiGl6PtXO4T83zo2UvXdmjOXVzpIYoUvfRgqpr3N+jicC0e3d8ro7A9DldZluPAALT8F4gMA0BcjwIAgjMIGK2MiQC0wpW74siML2P2NqACExraL0vjMDMPuKhF05p4oWrezS7+vvUMXO+rIkF1ehCW6TxfW7v0URgZn93fHkjAtOXJJljqwQQmFsltcFzCExDgBwPggACM4iYrQyJwLSC1fuiCEzvI7Y2IALTGlo2xZ5pAAAgAElEQVTvCyMwKx/x0h7NZ4vSiY33aF5qOqLR5T2arQ9EanVgjyYCs/J3J68dIDDzmhx9JyWAwExKbvkcAtMQIMeDIIDADCJmK0MiMK1g9b4oAtP7iK0NiMC0htb7wghM9yKeGrqi4aeKWtqjeS7W3tE+VWu+rNHSHs2hnl7NlvZo3hup655DmQ+CwMwcuTcvRGB6EyWDbJEAAnOLoDZ6DIFpCJDjQRBAYAYRs5UhEZhWsHpfFIHpfcTWBkRgWkPrfWEEpvsRLy4sqP8bxU32aLbpcmeklT2aPUcLqrK8RxOB6f7dcbVDBKarydCXLQIITEOyCExDgBwPggACM4iYrQyJwLSC1fuiCEzvI7Y2IALTGlrvCyMw8xnx4AunNPl8rJpTRXUN3GiPZq9q7iyo4+GCGrtaUx0WgZkqzqCKITCDipth+Snk5ncAgWnOkAr+E0Bg+p+xrQkRmLbI+l0Xgel3vjanQ2DapOt3bQSmH/mOnbqksefiTfZo3rq8R7OgNPZoIjD9uDuVmAKBWQnqvLOSBPgE5ib0T54+pw9+7NM6d3Hg2pP33HVEn3v8w+psbxUCs5LXl3fnhQACMy9JudcnAtO9TPLQEQIzDym52SMC081c8tAVAjMPKW2/x6nBMQ0/XdqjWdSOc7H2rLtHc6+GeiLNHYrUlGCPJgJz+7lw4ioBBCY3ITQCCMwtCMxHH/99Pfbx9+nwwX1rnkZghvaXDPMmIYDATEKNMyUCCEzuQRICCMwk1DhTIoDA5B4kJYDATEouX+cW5xfU/2Rpj2ashtdj7RyK1bwwWjbERPXVPZrTN/eqISqo560FVVVXbzgoAjNfd8ClbhGYLqVBL1kQQGAiMLd8z3raGjQ2Oavp2YUtn+FBCJQIIDC5B0kJIDCTkgv7HAIz7PxNpkdgmtAL+ywCM9z8S3s0J56PVXcqVmd/rI7Z82UwFlSj8229mtgXXd2j+Uikxs6WpWfO/N6X1HXsP6th7opGdtyk2e//Ue3+vgfDhcnk2yKAwNwWLh72gAACcwsC8/qvkF//9fHSUT6B6cFfBYxgnQAC0zpib1+AwPQ2WquDITCt4vW6OALT63itDofAtIo3V8XHTl3U2LOlPZpFtV2MtWvyxJr+LzXdqpn6Vh0Yea7sz2aqGjX+q19SQ+eOXM1Ms5UhgMCsDHfeWjkCCMxtsv/M55/QhUsD+sRH36vGxnoNX5ndZoX8Pl76F8KpmXnNzS/mdwg6rwiB1uZaTUzNa36Bu1ORAHL80rYdtboyOacFPvid4xSzb72hvlpN9TWanlnQ5Mx89g3wxtwSKAnMtuY6jYyH8893uQ3LscZL3xAu/bPy6PicY53RTqUJTA6Mqf/JPs281KemM+vv0by+x5Pf9SEdfu+7K902788BgdqaKjXW1yz9s3Iovzpa6kIZlTnXIRCswFzvh/Os8Fn9Kcuyv6GcPqdf+50v6bFffP/SD/GZmA7nvywa62o0O7+AhOK/SrZNoPQ31pnZBS0sIjC3DS/wA031V/+Hk0VxdwK/Ctsav7RPrK62eunvWbNz2O9tweNhNTfUBvXPd0SeDoEqXRUJkzPh/LtBOuTCq7Iwt6Bz/9Cn6v/wG+qZPLkugImaNg109mruUK923HO39n9Pr6qqq8KDxcQ3JFD65Hfpn3mmZsP5H2tLf4/mV7gEghWYSSMvic/rBSZfIU9KknMhEeAr5CGlne6sfIU8XZ6hVOMr5KEknf6cfIU8faahVOQr5KEknd6cZz7/p7r9uS+sKThau1Ntc5fLfv/aHs39pT2akTofLqhheY9meh1RKW8E+Ap53hKjX1MCCMxNCP7N157WbYf2X/sJ5KWvkJd+feQD71n6TwSm6RXkfAgEEJghpGxnRgSmHa6+V0Vg+p6wvfkQmPbY+l4Zgel7wnbmu/RvflW3XPzaUvHp6madfvCf68B7f0Sjpy7qytIezXh5j+ar/3979xqj6VnWAfze86m72z212y3tlspymHdoY4GmREn8wCeJ8RAwSoigiAgaIYBYmsgHNbVBIGoiighqTETTRE0IRIwheEyxpoV237GV3aW0uuyy5x3Y0+xuzTvM1J13Z3dn5nmvd5+57h9fmed6n+v3vzPd/e/svZe9QO8ezZPbO6W8pFPWv2qkrN95c8xLmtpaAQVma6PxYkECCsxrwD76tafK297z0Atf9YbX3/fC/ZcKzKBTaWw6AQVmukiHtpACc2jUqT5IgZkqzqEuo8AcKneqD1NgpopzqMtcOHmqrJo4V85vufGKn3vmyHg5/uhYufB0t6zbP32P5swrUo6vvKUc3TpaLry4U9bePVI2vfLFQ93Dhw1fQIE5fHOfeH0FFJgN/f0EZkNAj1choMCsIuaQJRWYIazphyow00cctqACM4w2/WAFZvqIwxbs3WF44/oV5dDxs3P+jIvnL5TDj4yVc2NjZfWz3bLt2O6y5uL4jOdPLdtYDm3qlHO3dcrK0U7Zet+IezTnLLw4vlCBuThy8paDE1BgNrRUYDYE9HgVAgrMKmIOWVKBGcKafqgCM33EYQsqMMNo0w9WYKaPOGzBhRSYs73M0a/tK6efGCvLv9Etmw7vLjdOHJjxZReWLC8H1nfKKfdohmU57MEKzGGL+7zrLaDAbJiAArMhoMerEFBgVhFzyJIKzBDW9EMVmOkjDltQgRlGm36wAjN9xGELDqrA7H/B3j2a4491y5I93bLxYLdsO32lezRHS9k1Utbf0ynrd94UtqfBgxdQYA7e1MR2CygwG+ajwGwI6PEqBBSYVcQcsqQCM4Q1/VAFZvqIwxZUYIbRph+swEwfcdiCUQVm/wt/7x7Nbrnw1Nj37tEc312Wlpn3aB5buaMc29qZukezUza98o6wvQ1uLqDAbG5owuISUGA2zEuB2RDQ41UIKDCriDlkSQVmCGv6oQrM9BGHLajADKNNP1iBmT7isAWHVWD2L/DCPZrdsbL6uavfo3n29k5Z1XGPZtghWOBgBeYC4Ty2aAUUmA2jU2A2BPR4FQIKzCpiDllSgRnCmn6oAjN9xGELKjDDaNMPVmCmjzhswetVYM620NGv7iunn+xO3aPZvcI9mqNT92iOlE2v6ZRVm9aF2Rh8dQEFphNSm4ACs2HiCsyGgB6vQkCBWUXMIUsqMENY0w9VYKaPOGxBBWYYbfrBCsz0EYct2KYCs3/J8X0Hy8nHd5ele8bKhiveo7mrnNzeKWVXp2y4Z6Tc4B7NsLPSP1iBOTRqH9QSAQVmwyAUmA0BPV6FgAKziphDllRghrCmH6rATB9x2IIKzDDa9IMVmOkjDluwzQVm/9Knj5wsJx4dm7pHc3e5ZbxbllzpHs07O2XtXe7RDDs4pRQFZqSu2W0UUGA2TEWB2RDQ41UIKDCriDlkSQVmCGv6oQrM9BGHLajADKNNP1iBmT7isAUXU4HZj/D/92h2y+pnu2Xb8W5Zc3F8xpedWraxHNo0Wibv0RwdKdteO1JKWRLmWdNgBWZNadu1J6DAbHgOFJgNAT1ehYACs4qYQ5ZUYIawph+qwEwfcdiCCsww2vSDFZjpIw5bcDEXmLOhTN6j+US3LH+mWzYf7paNEwdmfNmFJcvLgfVT92i+olM2vXrkqvdonjl0oixbu6qsWLc6LIPFOliBuViT894LFVBgLlRu6jkFZkNAj1choMCsIuaQJRWYIazphyow00cctqACM4w2/WAFZvqIwxbMVmD2Q43vPVDGv9otZc9Y2Xhwd9l2et9llt9eu6ucvHnmPZr7/+7LZeuXPv3CPyT0za0/UDbd/6GyfN2qsCwW22AF5mJLzPs2FVBgNhRUYDYE9HgVAgrMKmIOWVKBGcKafqgCM33EYQsqMMNo0w9WYKaPOGzB7AVmP9zpwyfL8f8cKxef6pZ1+7tXuEfzlrJh4lBZ9vz5GY/veckby473vzMsi8U2WIG52BLzvk0FFJgNBRWYDQE9XoWAArOKmEOWVGCGsKYfqsBMH3HYggrMMNr0gxWY6SMOW7C2ArMf8uLEhXL4kbFybuzK92hOP3Nixc3l+E8/MHWPZlgki2awAnPRROVFBySgwGwIqcBsCOjxKgQUmFXEHLKkAjOENf1QBWb6iMMWVGCG0aYfrMBMH3HYgrUXmLPB7v/bfyov+YffuqL5pfdoLn9Fp9x470hZtXFdWEZtHazAbGsy3itKQIHZUFaB2RDQ41UIKDCriDlkSQVmCGv6oQrM9BGHLajADKNNP1iBmT7isAUVmLPTTvzKW8rGiYMz/s+Da19Wlj4/Mes9mgfX7irj26fu0fz+kXLDzpvCMmvLYAVmW5LwHsMSUGA2lFZgNgT0eBUCCswqYg5ZUoEZwpp+qAIzfcRhCyoww2jTD1Zgpo84bEEF5uy0h/5td1n2ub8oW8a/XiaWrinf3vmDZccH3jX5xWcOnSzHevdoPj19j+busqQ8P2PQsZU7yrGto+XCnZ2y7u5OuXF0Z1iG12uwAvN6yfvc6yWgwGwor8BsCOjxKgQUmFXEHLKkAjOENf1QBWb6iMMWVGCG0aYfrMBMH3HYggrM5rQXJs6XI5P3aI6V1c92y03Hd5fVF78zY/B3l91YDm/qlLO3d8qq0U6KezQVmM3PjgmLS0CB2TAvBWZDQI9XIaDArCLmkCUVmCGs6YcqMNNHHLagAjOMNv1gBWb6iMMWVGDG0B796t5y6omxsuIb3bL5yO7L/jr6hSUryoENnXLq1k5Z9vJO2XzvSFm5yO7RVGDGnB1T2yugwGyYjQKzIaDHqxBQYFYRc8iSCswQ1vRDFZjpIw5bUIEZRpt+sAIzfcRhCyoww2hnDD6590D5zuPdsmRPt2w42C3bzuy77IMPrn3p1D2aI2XDPZ1yw+3bhvNyC/wUBeYC4Ty2aAUUmA2jU2A2BPR4FQIKzCpiDllSgRnCmn6oAjN9xGELKjDDaNMPVmCmjzhsQQVmGO1VB585dGLqHs2xsm5/t9wyPts9mreWY9s6k/dorr2rUza17B5NBeb1OTs+9foJKDAb2iswGwJ6vAoBBWYVMYcsqcAMYU0/VIGZPuKwBRWYYbTpBysw00cctqACM4x2XoMvnDtfjn5lrJztdsvq53r3aHaveI/mudtHy8rRket+j6YCc14R++IEAgrMhiEqMBsCerwKAQVmFTGHLKnADGFNP1SBmT7isAUVmGG06QcrMNNHHLagAjOMtvHgo4/vLaee7E7do9m97B7N80tWlIMbRqfu0Rwpm+/tlJUb1zb+3LkOUGDOVcrXZRFQYDZMUoHZENDjVQgoMKuIOWRJBWYIa/qhCsz0EYctqMAMo00/WIGZPuKwBRWYYbQDH3xy77em7tEcm8M9mp2y4VUj5Ybb4u7RVGAOPGIDWy6gwGwYkAKzIaDHqxBQYFYRc8iSCswQ1vRDFZjpIw5bUIEZRpt+sAIzfcRhCyoww2jDB0/eo/noWLn4dLes+1bvHs1uWVKen/G5x1b27tEc/d49mnePlE2dnQN7LwXmwCgNWiQCCsyGQSkwGwJ6vAoBBWYVMYcsqcAMYU0/VIGZPuKwBRWYYbTpBysw00cctqACM4x26IN792geeWSsTIx1y6qr3qM5Ws7u7JTVnZGy9bUjC35PBeaC6Ty4SAUUmA2DU2A2BPR4FQIKzCpiDllSgRnCmn6oAjN9xGELKjDDaNMPVmCmjzhsQQVmGG0rBh99bE85/eRYWf5Mt2w+Mvs9mgc2jJbTt3bKspd3yuZ7R+Z8j6YCsxURe4khCigwG2IrMBsCerwKAQVmFTGHLKnADGFNP1SBmT7isAUVmGG06QcrMNNHHLagAjOMtpWDe/dojj/WLUv3dsvGg92y9cw3LnvPg2tfWsa3d0rZ1SkbXzVS1l3hHs0Tj3+9rDg/UZ7fflNZd9vWVu476JfasWXNoEeat4gEFJgNw1JgNgT0eBUCCswqYg5ZUoEZwpp+qAIzfcRhCyoww2jTD1Zgpo84bEEFZhjtohjcf4/mjvFuKde4R3P5utVl6e9/uGw7ve+FHf979K3lRb/0lkWxc5OXVGA20Vv8zyowG2aowGwI6PEqBBSYVcQcsqQCM4Q1/VAFZvqIwxZUYIbRph+swEwfcdiCCsww2kU5+MLZ8+XIV7rl3NhYWfNct2w7vrusvvjdGbtMLFlVVjx/9rL9Dj3w2fQ/ianAXJTHemAvrcBsSKnAbAjo8SoEFJhVxByypAIzhDX9UAVm+ojDFlRghtGmH6zATB9x2IIKzDDaNINn3qO5u2yc+Pasuz3z5o+Vm153V5q9Z1tEgZk63msup8C8JtHVv0CB2RDQ41UIKDCriDlkSQVmCGv6oQrM9BGHLajADKNNP1iBmT7isAUVmGG0aQcfvf/XyotOPHbZfs+9/Q/Klle/NO3evcUUmKnjveZyCsxrEikwpwW2blhVxk9PlLMTFxuqebw2AQVmbYkPbl8F5uAsa5qkwKwp7cHuqsAcrGdN0xSYNaU92F0VmIP1rGHa/372i2XXP390xqqH1txZ1n38k+nXV2Cmj/iqCyowG+bvJzAbAnq8CgEFZhUxhyypwAxhTT9UgZk+4rAFFZhhtOkHKzDTRxy2oAIzjDb14F6JuWrs38vyiVPl1OY7yvqffGNZf8fNqXfuLafATB+xAjMyYgVmpK7ZWQQUmFmSHP4eCszhm2f4RAVmhhSvzw4KzOvjnuFTFZgZUrw+Oygwr497hk9dtWJpWb9mRTl88vJ/0CfDfrPtoMDMmuzc9vITmHNzuuJXKTAbAnq8CgEFZhUxhyypwAxhTT9UgZk+4rAFFZhhtOkHKzDTRxy2oAIzjDb9YAVm+ogt2CegwGx4JBSYDQE9XoWAArOKmEOWVGCGsKYfqsBMH3HYggrMMNr0gxWY6SMOW1CBGUabfrACM33EFlRgDvYMKDAH62laTgEFZs5ch7GVAnMYyvk+Q4GZL9NhbaTAHJZ0vs9RYObLdFgbKTCHJZ3vcxSY+TK10dUF/ARmwxOiwGwI6PEqBBSYVcQcsqQCM4Q1/VAFZvqIwxZUYIbRph+swEwfcdiCCsww2vSDFZjpI7Zgn4ACs+GRUGA2BPR4FQIKzCpiDllSgRnCmn6oAjN9xGELKjDDaNMPVmCmjzhsQQVmGG36wQrM9BFbUIE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"source": [
"al.printSyst(A,b)\n",
"al.SolOfSyst(alpha, A,b)\n",
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]
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"source": [
"### **EXERCICE 2**\n",
"\n",
"Pour chacun des cas ci-dessous, déterminer la/les solution(s) des systèmes. \n",
"\n",
"$$ \n",
"a)\\quad \\begin{cases}\n",
"x_1 - x_2 + 2x_3 &=0\\\\\n",
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"2x_1 + 5x_2 &=-2\n",
"\\end{cases} \\hspace{1cm} b) \\quad \\begin{cases}\n",
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"\\end{cases} \\hspace{1cm} c) \\quad \\begin{cases}\n",
"x_1 + x_2 -2x_3 &=-1\\\\\n",
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"\\end{cases} \\hspace{1cm}\n",
"$$\n"
]
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{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 8,
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"b=[1,1,1]\n"
]
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- "execution_count": null,
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\"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmap\"}], \"heatmapgl\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmapgl\"}], \"histogram\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"histogram\"}], \"histogram2d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2d\"}], \"histogram2dcontour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2dcontour\"}], \"mesh3d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"mesh3d\"}], \"parcoords\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"parcoords\"}], \"pie\": [{\"automargin\": true, \"type\": \"pie\"}], \"scatter\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter\"}], \"scatter3d\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter3d\"}], \"scattercarpet\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattercarpet\"}], \"scattergeo\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergeo\"}], \"scattergl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergl\"}], \"scattermapbox\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattermapbox\"}], \"scatterpolar\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolar\"}], \"scatterpolargl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolargl\"}], \"scatterternary\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterternary\"}], \"surface\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"surface\"}], \"table\": [{\"cells\": {\"fill\": {\"color\": \"#EBF0F8\"}, \"line\": {\"color\": \"white\"}}, \"header\": {\"fill\": {\"color\": \"#C8D4E3\"}, \"line\": {\"color\": \"white\"}}, \"type\": \"table\"}]}, \"layout\": {\"annotationdefaults\": {\"arrowcolor\": \"#2a3f5f\", \"arrowhead\": 0, \"arrowwidth\": 1}, \"coloraxis\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"colorscale\": {\"diverging\": [[0, \"#8e0152\"], [0.1, \"#c51b7d\"], [0.2, \"#de77ae\"], [0.3, \"#f1b6da\"], [0.4, \"#fde0ef\"], [0.5, \"#f7f7f7\"], [0.6, \"#e6f5d0\"], [0.7, \"#b8e186\"], [0.8, \"#7fbc41\"], [0.9, \"#4d9221\"], [1, \"#276419\"]], \"sequential\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"sequentialminus\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"width\": 800},\n",
+ " {\"responsive\": true}\n",
+ " ).then(function(){\n",
+ " \n",
+ "var gd = document.getElementById('b9d4cff4-98b4-4571-bfbc-451f00641992');\n",
+ "var x = new MutationObserver(function (mutations, observer) {{\n",
+ " var display = window.getComputedStyle(gd).display;\n",
+ " if (!display || display === 'none') {{\n",
+ " console.log([gd, 'removed!']);\n",
+ " Plotly.purge(gd);\n",
+ " observer.disconnect();\n",
+ " }}\n",
+ "}});\n",
+ "\n",
+ "// Listen for the removal of the full notebook cells\n",
+ "var notebookContainer = gd.closest('#notebook-container');\n",
+ "if (notebookContainer) {{\n",
+ " x.observe(notebookContainer, {childList: true});\n",
+ "}}\n",
+ "\n",
+ "// Listen for the clearing of the current output cell\n",
+ "var outputEl = gd.closest('.output');\n",
+ "if (outputEl) {{\n",
+ " x.observe(outputEl, {childList: true});\n",
+ "}}\n",
+ "\n",
+ " })\n",
+ " };\n",
+ " });\n",
+ " </script>\n",
+ " </div>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"al.printSyst(A,b)\n",
"al.Plot3DSys(-10,10,100,A,b)"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 10,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "La suite entrée n'est pas une solution de l'équation 1\n",
+ "La suite entrée n'est pas une solution de l'équation 2\n",
+ "La suite entrée n'est pas une solution de l'équation 3\n",
+ "Ce n'est pas une solution du système\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "False"
+ ]
+ },
+ "execution_count": 10,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"alpha = [1,1,1]\n",
"al.SolOfSyst(alpha, A,b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### **EXERCICE 3**\n",
"#code 1.2.Ex3\n",
"\n",
"À l'aide des graphes interactifs ci-dessous, trouver les valeurs des paramètres $h$ et $k$ pour que les systèmes a), b), c) e d) admettent, si possible,\n",
"1. aucune solution\n",
"2. une unique solution\n",
"3. une infinité de solution \n",
"\n",
"\n",
"$$ \n",
"a)\\begin{cases}\n",
"x_1 +5 x_2&=h\\\\\n",
"-2x_1 -10 x_2&=18\n",
"\\end{cases} \\hspace{1cm} b) \\begin{cases}\n",
"hx_1 + x_2&=3\\\\\n",
"-2x_1 - x_2&=-1\n",
"\\end{cases}\\hspace{1cm} c) \\begin{cases}\n",
"3x_1 + hx_2&=1\\\\\n",
"x_1 + 3x_2&=h\n",
"\\end{cases}\\hspace{1cm} d) \\begin{cases}\n",
"kx_1 + x_2&=h\\\\\n",
"3x_1 -5x_2&=2\n",
"\\end{cases}\n",
"$$"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 11,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ " <script type=\"text/javascript\">\n",
+ " window.PlotlyConfig = {MathJaxConfig: 'local'};\n",
+ " if (window.MathJax) {MathJax.Hub.Config({SVG: {font: \"STIX-Web\"}});}\n",
+ " if (typeof require !== 'undefined') {\n",
+ " require.undef(\"plotly\");\n",
+ " requirejs.config({\n",
+ " paths: {\n",
+ " 'plotly': ['https://cdn.plot.ly/plotly-latest.min']\n",
+ " }\n",
+ " });\n",
+ " require(['plotly'], function(Plotly) {\n",
+ " window._Plotly = Plotly;\n",
+ " });\n",
+ " }\n",
+ " </script>\n",
+ " "
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"import plotly as py\n",
"import numpy as np\n",
"plotly.offline.init_notebook_mode(connected=True)\n",
"import plotly.graph_objs as go\n",
"from ipywidgets import interactive, HBox, VBox, widgets, interact, FloatSlider"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## CASE a)"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 12,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/latex": [
+ "$\\begin{cases}x_1+5x_2=0\\\\-2x_1-10x_2=18\\\\\\end{cases}$"
+ ],
+ "text/plain": [
+ "<IPython.core.display.Latex object>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ },
+ {
+ "data": {
+ "application/vnd.jupyter.widget-view+json": {
+ "model_id": "f1d0199fde4e4ed5bf2774cdb514e043",
+ "version_major": 2,
+ "version_minor": 0
+ },
+ "text/plain": [
+ "VBox(children=(FigureWidget({\n",
+ " 'data': [{'name': 'a) Droite 1',\n",
+ " 'type': 'scatter',\n",
+ " …"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
"source": [
"A=[[1, 5], [-2, -10]] # we initialize the problem. The values of h and k must be fixed to one specific value here\n",
"b=[0, 18]\n",
"al.printSyst(A, b) # the system printed below shows the values of h and k inserted here!!\n",
"\n",
"data=[]\n",
"x=np.linspace(-5,5,11)\n",
"m=len(A)\n",
"MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n",
"MatCoeff=np.array(MatCoeff)\n",
"\n",
"for i in range(len(MatCoeff)):\n",
" trace=go.Scatter(x=x, y=(MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='a) Droite %d'%(i+1))\n",
" data.append(trace)\n",
"\n",
"f=go.FigureWidget(data=data,\n",
" layout=go.Layout(xaxis=dict(\n",
" range=[-5, 5]\n",
" ),\n",
" yaxis=dict(\n",
" range=[-10, 10]\n",
" ) )\n",
"\n",
")\n",
"#def update_y(coeff, cof):\n",
" # MatCoeff= [[coeff, 1, cof]]\n",
" # MatCoeff=np.array(MatCoeff)\n",
" # f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
"def update_y(h):\n",
" MatCoeff = [[1, 5, h]]\n",
" MatCoeff=np.array(MatCoeff)\n",
" f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
" \n",
"freq_slider = interactive(update_y, h=(-15, 15, 1/2)) \n",
"vb = VBox((f, freq_slider))\n",
"vb.layout.align_items = 'center'\n",
"vb"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## CASE b)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"A=[[1, 1], [-2,-2]] # we initialize the problem. The value of h is fixed\n",
"b=[3, -1]\n",
"al.printSyst(A, b) # the system printed below shows the value of h inserted here\n",
"\n",
"m=len(A)\n",
"MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n",
"MatCoeff=np.array(MatCoeff)\n",
"data=[]\n",
"x=np.linspace(-5,5,11)\n",
"MatCoeff=np.array(MatCoeff)\n",
"for i in range(len(MatCoeff)):\n",
" trace=go.Scatter(x=x, y= (MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='b) Droite %d'%(i+1))\n",
" data.append(trace)\n",
" \n",
"f=go.FigureWidget(data=data,\n",
" layout=go.Layout(xaxis=dict(\n",
" range=[-5, 5]\n",
" ),\n",
" yaxis=dict(\n",
" range=[-10, 10]\n",
" ) )\n",
" \n",
")\n",
"#def update_y(coeff, cof):\n",
" # MatCoeff= [[coeff, 1, cof]]\n",
" # MatCoeff=np.array(MatCoeff)\n",
" # f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
"#coefficients=[[h,1,3]]\n",
"def mat(k):\n",
" h=k\n",
" MatCoeff=[[h,1,3]]\n",
" return MatCoeff\n",
"def update_y(h):\n",
" MatCoeff= mat(h)\n",
" MatCoeff=np.array(MatCoeff)\n",
" f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
" \n",
"freq_slider = interactive(update_y, h=(-10, 10, 1/2)) \n",
"\n",
"vb = VBox((f, freq_slider))\n",
"vb.layout.align_items = 'center'\n",
"vb"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## CASE c)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"A=[[3, 1], [1, 3]] # we initialize the problem. The values of h and k are fixed\n",
"b=[1, 1]\n",
"al.printSyst(A, b) # the system printed below shows the values of h and k inserted here\n",
"\n",
"m=len(A)\n",
"MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n",
"MatCoeff=np.array(MatCoeff)\n",
"data=[]\n",
"x=np.linspace(-25,25,101)\n",
"MatCoeff=np.array(MatCoeff)\n",
"for i in range(len(MatCoeff)):\n",
" trace=go.Scatter(x=x, y= (MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='c) Droite %d'%(i+1))\n",
" data.append(trace)\n",
" \n",
"f=go.FigureWidget(data=data,\n",
" layout=go.Layout(xaxis=dict(\n",
" range=[-25, 25]\n",
" ),\n",
" yaxis=dict(\n",
" range=[-50, 50]\n",
" ) )\n",
" \n",
")\n",
"#def update_y(coeff, cof):\n",
" # MatCoeff= [[coeff, 1, cof]]\n",
" # MatCoeff=np.array(MatCoeff)\n",
" # f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
"def mat(h):\n",
" MatCoeff= [[h, 3, 1],[3, 1, h] ]\n",
" return MatCoeff\n",
"\n",
"def update_y(h):\n",
" MatCoeff= mat(h)\n",
" MatCoeff=np.array(MatCoeff)\n",
" f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
" f.data[1].y=(MatCoeff[1,2]-MatCoeff[1,0]*x)/MatCoeff[1,1]\n",
"\n",
"freq_slider = interactive(update_y, h=(-20, 20, 1)) \n",
"\n",
"vb = VBox((f, freq_slider))\n",
"vb.layout.align_items = 'center'\n",
"vb"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## CASE d)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"A=[[1, 1], [3, -5]] # we initialize the problem. The values of h and k are fixed\n",
"b=[1, 2]\n",
"al.printSyst(A, b) # the system printed below shows the values of h and k inserted here\n",
"\n",
"m=len(A)\n",
"MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n",
"MatCoeff=np.array(MatCoeff)\n",
"data=[]\n",
"x=np.linspace(-15,15,101)\n",
"MatCoeff=np.array(MatCoeff)\n",
"for i in range(len(MatCoeff)):\n",
" trace=go.Scatter(x=x, y= (MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='d) Droite %d'%(i+1))\n",
" data.append(trace)\n",
" \n",
"f=go.FigureWidget(data=data,\n",
" layout=go.Layout(xaxis=dict(\n",
" range=[-15, 15]\n",
" ),\n",
" yaxis=dict(\n",
" range=[-10, 10]\n",
" ) )\n",
" \n",
")\n",
"#def update_y(coeff, cof):\n",
" # MatCoeff= [[coeff, 1, cof]]\n",
" # MatCoeff=np.array(MatCoeff)\n",
" # f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
"def update_y(h, k):\n",
" MatCoeff= [[h, 1, k],[2, -5, 5] ]\n",
" MatCoeff=np.array(MatCoeff)\n",
" f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
"\n",
" \n",
" f.data[1].y=(MatCoeff[1,2]-MatCoeff[1,0]*x)/MatCoeff[1,1]\n",
"\n",
"freq_slider = interactive(update_y, h=(-10, 10, 1/10),k=(-10, 10, 1))\n",
"\n",
"vb = VBox((f, freq_slider))\n",
"vb.layout.align_items = 'center'\n",
"vb"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercice 4\n",
"\n",
"À l'aide des graphes interactifs ci-dessous, trouver les valeurs des paramètre $h$ pour que le système admet, si possible,\n",
"1. aucune solution\n",
"2. une unique solution\n",
"3. une infinité de solution \n",
"\n",
"$$ \n",
"\\begin{cases}\n",
"hx_1 -2 x_2 &=4\\\\\n",
"-2x_1 +h x_2&=-4\\\\\n",
"x_1 - x_2 &=h\n",
"\\end{cases} \\hspace{1cm}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"A=[[1, -2], [-2, 1], [1, -1]] # we initialize the problem. The values of h and k are fixed\n",
"b=[4, -4, 2]\n",
"al.printSyst(A, b) # the system printed below shows the values of h and k inserted here\n",
"\n",
"m=len(A)\n",
"MatCoeff = [A[i]+[b[i]]for i in range(m)] #becomes augmented matrix\n",
"MatCoeff=np.array(MatCoeff)\n",
"data=[]\n",
"x=np.linspace(-25,25,101)\n",
"MatCoeff=np.array(MatCoeff)\n",
"for i in range(len(MatCoeff)):\n",
" trace=go.Scatter(x=x, y=(MatCoeff[i,2]-MatCoeff[i,0]*x)/MatCoeff[i,1], name='c) Droite %d'%(i+1))\n",
" data.append(trace)\n",
" \n",
"f=go.FigureWidget(data=data,\n",
" layout=go.Layout(xaxis=dict(\n",
" range=[-25, 25]\n",
" ),\n",
" yaxis=dict(\n",
" range=[-50, 50]\n",
" ) )\n",
" \n",
")\n",
"#def update_y(coeff, cof):\n",
" # MatCoeff= [[coeff, 1, cof]]\n",
" # MatCoeff=np.array(MatCoeff)\n",
" # f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
"def mat(h):\n",
" MatCoeff= [[h, -2, 4], [-2, h, -4], [1, -1, h]]\n",
" return MatCoeff\n",
"\n",
"def update_y(h):\n",
" MatCoeff= mat(h)\n",
" MatCoeff=np.array(MatCoeff)\n",
" f.data[0].y=(MatCoeff[0,2]-MatCoeff[0,0]*x)/MatCoeff[0,1]\n",
" f.data[1].y=(MatCoeff[1,2]-MatCoeff[1,0]*x)/MatCoeff[1,1]\n",
" f.data[2].y=(MatCoeff[2,2]-MatCoeff[2,0]*x)/MatCoeff[2,1]\n",
"\n",
"freq_slider = interactive(update_y, h=(-20, 20, 1)) \n",
"\n",
"vb = VBox((f, freq_slider))\n",
"vb.layout.align_items = 'center'\n",
"vb"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[Passez au notebook du chapitre 1.3-4: Notation Matricielle](./1.3-4.%20Notation%20Matricielle.ipynb)"
]
}
],
"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": "3.7.4"
+ "version": "3.6.9"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
diff --git a/Chapitre 3 - Espace vectoriel/Untitled.ipynb b/Chapitre 3 - Espace vectoriel/Untitled.ipynb
deleted file mode 100644
index a4c7d81..0000000
--- a/Chapitre 3 - Espace vectoriel/Untitled.ipynb
+++ /dev/null
@@ -1,46 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": [
- "v=[1,2,3]\n",
- "w=[0,-3,4]\n",
- "#Quel vecteur on ajoute à v pour obtenir w?\n",
- "\n",
- "u=[-1, 5,1]\n",
- "#maintenant que l'on a plus que des vecteurs, on peut utiliser [...]"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": null,
- "metadata": {},
- "outputs": [],
- "source": []
- }
- ],
- "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": "3.6.8"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}

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