diff --git "a/Chapitre 1 - Systemes equations lineaires/1.1. Introduction et d\303\251finition.ipynb" "b/Chapitre 1 - Systemes equations lineaires/1.1. Introduction et d\303\251finition.ipynb"
index 2c9d3a6..258dc83 100644
--- "a/Chapitre 1 - Systemes equations lineaires/1.1. Introduction et d\303\251finition.ipynb"	
+++ "b/Chapitre 1 - Systemes equations lineaires/1.1. Introduction et d\303\251finition.ipynb"	
@@ -1,311 +1,302 @@
 {
  "cells": [
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "# Concept(s)-clé(s) et théorie\n",
     "\n",
     "### DÉFINITION 1 :\n",
     "\n",
     "Une *équation linéaire* aux inconnues $x_1,\\ldots,x_n$ à coefficients réels est une équation de la forme\n",
     "\n",
     "$$a_1x_1+a_2x_2+\\cdots+a_nx_n=b,$$ \n",
     "où $a_1,a_2,\\ldots,a_n,b\\in \\mathbb{R}.$\n",
     " \n",
     "---\n",
     "### DÉFINITION 2 :\n",
     "\n",
     "On appelle *système d'équations linéaires*  (ou simplement système linéaire) une famille d'équations linéaires aux inconnues $x_1,\\ldots,x_n$ à coefficients réels de la forme  \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",
     "Aussi, on dit qu'une suite ordonnée de $n$ nombres réels $\\alpha=(\\alpha_1,\\ldots,\\alpha_n)$ est une *solution du système linéaire* $S$ si toutes les égalités du système sont vérifiées lorsque l'on remplace $x_j$ par $\\alpha_j,$ ceci pout tout $1\\leq j\\leq n.$"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "import Librairie.AL_Fct as al\n",
     "#from IPython.core.magic import register_cell_magic\n",
     "#from IPython.display import HTML, display\n",
     "#import numpy as np"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### EXEMPLE 1\n",
     "\n",
     "Dans ce premier exemple nous nous familiarisons avec les équations et les ensembles de solutions. Soit  \n",
     "$$ \n",
     "a_{1}x_{1} + a_{2}x_{2} + \\ldots a_{n}x_{n}=b_1.\n",
     "$$  \n",
     "On utilise *la syntaxe suivante pour définir les coefficients* de l'équation \n",
     "\n",
     "$$\n",
     "\\begin{align*}\n",
     "A&=[a_1, a_2, \\ldots, a_n]\\\\\n",
     "b&=[b_1].\n",
     "\\end{align*}\n",
     "$$\n",
     "\n",
     "---\n",
     "Dans la case ci-dessous, entrer les coefficients de l'équation \n",
     "$$3x_1 + 2x_2=7$$\n",
     "\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "al.bgc('seashell')\n",
     "#Toutes les valeurs sont initialisées à 1\n",
     "\n",
     "A = [1] \n",
     "b = [1]\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "al.printEq(A,b)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "On utilise *la syntaxe suivante pour entrer une solution* d'une équation\n",
     "$$\\rm{alpha}=[\\alpha_1, \\alpha_2, \\ldots, \\alpha_n]$$"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "al.bgc('seashell')\n",
     "#Toutes les valeurs sont initialisées à 1\n",
     "\n",
-    "alpha = [1] #solution"
+    "alpha = [1, 1] #solution"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
-    "isSol = [al.SolOfEq(alpha, A+b,1)]"
+    "isSol = [al.SolOfEq(alpha, A+b, 1)]"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### **EXERCICE 1**\n",
     "\n",
     "Enter l'équation $$ \\frac{2}{5}x_1 -4x_2 + x_3 = 8$$ et donner une solution $$\\alpha=(\\alpha_1, \\alpha_2, \\alpha_3).$$\n",
     "\n",
     "Vous pouvez aussi adapter le code à l'équation de votre choix."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "al.bgc('seashell')\n",
     "\n",
     "#Par défaut, les valeurs sont fixées à 1\n",
     "\n",
     "A = [1] \n",
     "b =[1]\n",
     "alpha = [1] #solution "
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "al.printEq(A,b)\n",
     "isSol=[al.SolOfEq(alpha, A+b,1)]"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### EXEMPLE 2\n",
     "\n",
     "Dans cet exercice nous nous familiarisonns avec les systèmes d'équations. La partie ci-dessous vous demande de rentrer un système d'équation. \n",
     "\n",
     "Soit\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",
     "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",
     "Essayer d'entrer le système d'équations ci-dessous\n",
     "\n",
     "$$\\begin{cases}\n",
-    "x_1 &-3 x_2 &&=4\\\\\n",
-    "-x_1 & + 4 x_2&&= 5\n",
+    "x_1 &- & 3 x_2 && = 4\\\\\n",
+    "-x_1 & + & 4 x_2 && = 5\n",
     "\\end{cases}\n",
     "$$"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "al.bgc('seashell')\n",
     "\n",
     "#Par défaut, les valeurs sont fixées à 1\n",
     "\n",
     "A = [ [1, 1], [1, 1]] \n",
-    "b=[1,1] \n",
-    "alpha = [1,1] #solution"
+    "b=[1, 1] \n",
+    "alpha = [1, 1] #solution"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "al.printSyst(A,b)"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "al.SolOfSyst(alpha, A,b)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### **EXERCICE 2**\n",
     "   \n",
     "Entrer le système suivant et donner une solution du système.\n",
     "\n",
     "$$\\begin{cases}\n",
     "&2x_1 -3 x_2   + x_3&&=-5\\\\\n",
     "&-\\dfrac{1}{3}x_1  +  x_3&&= 2\\\\\n",
     "&x_1 + 4x_2 -x_3 &&=0\n",
     "\\end{cases}\n",
     "$$\n",
     "\n",
     "Vous pouvez aussi adapter le code à l'équation de votre choix."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "al.bgc('seashell')\n",
     "#Par défaut, les valeurs sont fixées à 1\n",
     "\n",
     "A = [[1,1,1], [1,1,1], [1,1,1]]\n",
     "b =[1,1,1]\n",
     "alpha =[1,1,1] #solution\n"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "al.printSyst(A,b)\n",
     "al.SolOfSyst(alpha, A,b)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "[Passez au notebook du chapitre 1.2: Nombre de solutions d'un système](./1.2.%20Nombre%20de%20solution%20d'un%20système.ipynb)"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "b=al.np.array([1,2,3])"
-   ]
-  },
   {
    "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"
+   "version": "3.7.4"
   }
  },
  "nbformat": 4,
  "nbformat_minor": 4
 }