diff --git "a/Chapitre 2 - Algebre matricielle/2.1 Addition, multiplication par un scalaire, transpos\303\251e.ipynb" "b/Chapitre 2 - Algebre matricielle/2.1 Addition, multiplication par un scalaire, transpos\303\251e.ipynb"
index 7482811..63e4109 100644
--- "a/Chapitre 2 - Algebre matricielle/2.1 Addition, multiplication par un scalaire, transpos\303\251e.ipynb"	
+++ "b/Chapitre 2 - Algebre matricielle/2.1 Addition, multiplication par un scalaire, transpos\303\251e.ipynb"	
@@ -1,164 +1,274 @@
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  "cells": [
   {
    "cell_type": "markdown",
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    "source": [
     "# **Concept(s)-clé(s) et théorie**\n",
     "\n",
-    "L'*ensemble des matrices* de tailles $m\\times n$ à coefficients réels se note\n",
-    "$$M_{m\\times n}(\\mathbb{R}).$$\n",
+    "L'*ensemble des matrices* de tailles $m\\times n$ à coefficients réels se note $\\mathcal{M}_{m\\times n}(\\mathbb{R}).$\n",
     "\n",
+    "On rappelle que pour une matrice $A\\in \\mathcal{M}_{m\\times n}(\\mathbb{R})$ on a $A=(a_{ij})$ avec $1\\leq i \\leq m$ et $1\\leq j\\leq n$. On utilise aussi $(A)_{ij}$ pour dénoter la composante $a_{ij}$ de la matrice $A$.\n",
     "\n",
     "\n",
-    "Soient deux matrices $A,B\\in M_{m\\times n}(\\mathbb{R})$ et $\\lambda\\in\\mathbb{R}$ on définit:\n",
     "\n",
-    "$\\bullet \\hskip.5em A+B\\in M_{m\\times n}(\\mathbb{R})$ par\n",
-    "$$(A+B)_{ij}=A_{ij}+B_{ij},$$ pour tout $1≤i≤m$ et tout $1≤j≤n$;\n",
+    "Soient deux matrices $A,B\\in \\mathcal{M}_{m\\times n}(\\mathbb{R})$ et soit un scalaire $\\lambda\\in\\mathbb{R}$ on définit:\n",
     "\n",
-    "$\\bullet \\hskip.5em\\lambda A\\in M_{m\\times n}(\\mathbb{R})$ par\n",
-    "$$(\\lambda A)_{ij}=\\lambda A_{ij},$$\n",
-    "pour tout $1≤i≤m$ et tout $1≤j≤n$;\n",
+    "$\\bullet$ l'addition $\\hskip.5em A+B\\in \\mathcal{M}_{m\\times n}(\\mathbb{R})$ par\n",
+    "$$(A+B)_{ij}=a_{ij}+b_{ij},$$ pour tout $1\\leq i\\leq m$ et tout $1\\leq j \\leq n$;\n",
     "\n",
-    "$\\bullet\\hskip.5em$ la transposée de $A$, notée $A^T$, par\n",
-    "$$(A^T)_{ij}=A_{ji},$$\n",
-    "pour tout $1≤i≤n$ et tout $1≤j≤m$. Il est important de remarquer que $A^T\\in M_{n\\times m}(\\mathbb{R})$ dans cette situation."
+    "$\\bullet$ la multiplication par un scalaire $\\hskip.5em\\lambda A\\in \\mathcal{M}_{m\\times n}(\\mathbb{R})$ par\n",
+    "$$(\\lambda A)_{ij}=\\lambda a_{ij},$$\n",
+    "pour tout $1\\leq i\\leq m$ et tout $1\\leq j \\leq n$;\n",
+    "\n",
+    "\n",
+    "\n",
+    "On peut définir la transposée de $A$, que l'on note $A^T$, par\n",
+    "$$(A^T)_{ij}=a_{ji},$$\n",
+    "pour tout $1\\leq i\\leq m$ et tout $1\\leq j \\leq n$. On remarque que $A^T\\in \\mathcal{M}_{n\\times m}(\\mathbb{R})$ dans cette situation."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 1,
    "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"
+    },
+    {
+     "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 Librairie.AL_Fct as al\n",
     "import Corrections.corrections as corrections"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### **Exercice 1**\n",
     "\n",
-    "Rentrer les tailles de la transposée de la matrice ci-dessous."
+    "Trouver la dimension de la **Transposée de la matrice** donnée ci-dessous en remplissant les deux champs dans lesquels vous pouvez rentrer une valeur pour $m$ et $n$. \n",
+    "\n",
+    "Vérifier en cliquant sur **Run Interact**"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 2,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\left(\\begin{array}{cccccc}  5 & 2 & 18 & 35 & 23 & 93 \\\\-24 & -71 & -38 & 58 & -28 & 68  \\end{array}\\right)$"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Latex object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "A=al.randomA()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 3,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "43d1984827e048348f76def503c8831d",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "IntText(value=1, description='m:')"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
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+       "IntText(value=1, description='n:')"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "2f502e8cf0544c6e9c0ba213ad6c27f1",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "interactive(children=(Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widge…"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "al.dimensionA(A.transpose())"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### **Exercice 2**\n",
     "\n",
-    "Soient $A,B\\in M_{4\\times 2}(\\mathbb{R})$ données par\n",
+    "Soient $A,B\\in \\mathcal{M}_{4\\times 2}(\\mathbb{R})$ données par\n",
     "$$\n",
-    "A=\\begin{bmatrix}\n",
+    "A=\\begin{pmatrix}\n",
     "1 & -12 \\\\\n",
     "6 & 4\\\\\n",
     "-5 & 2\\\\\n",
     "0 & -2\n",
-    "\\end{bmatrix}\\hskip2em\n",
-    "B=\\begin{bmatrix}\n",
+    "\\end{pmatrix}\\hskip2em\n",
+    "B=\\begin{pmatrix}\n",
     "0 & 4\\\\\n",
     "-2 & -1\\\\\n",
     "1 & -1\\\\\n",
     "1 & 3\n",
-    "\\end{bmatrix}\n",
+    "\\end{pmatrix}\n",
     "$$\n",
     "\n",
     "Cocher la proposition qui est correcte."
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "corrections.Ex2Chapitre2_1()"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "### **Exercice 3**\n",
     "\n",
-    "Soient $A,B\\in M_{4\\times 2}(\\mathbb{R})$ données par\n",
+    "Soient $A,B\\in \\mathcal{M}_{4\\times 2}(\\mathbb{R})$ données par\n",
     "$$\n",
-    "A=\\begin{bmatrix}\n",
+    "A=\\begin{pmatrix}\n",
     "1 & -12 \\\\\n",
     "6 & 4\\\\\n",
     "-5 & 2\\\\\n",
     "0 & -2\n",
-    "\\end{bmatrix}\\hskip2em\n",
-    "B=\\begin{bmatrix}\n",
+    "\\end{pmatrix}\\hskip2em\n",
+    "B=\\begin{pmatrix}\n",
     "0 & 4\\\\\n",
     "-2 & -1\\\\\n",
     "1 & -1\\\\\n",
     "1 & 3\n",
-    "\\end{bmatrix}\n",
+    "\\end{pmatrix}\n",
     "$$\n",
     "\n",
     "Soit $C$ donnée par $C=(3(-2A^T) + (-2B)^T)^T$. \n",
     "\n",
     "Alors $C_{32}$vaut"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
     "corrections.Ex3Chapitre2_1()"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
     "[Passez au notebook du chapitre 2.2: Multiplication de matrices](./2.2%20Multiplication%20de%20matrices.ipynb)"
    ]
   }
  ],
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    "mimetype": "text/x-python",
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.6.9"
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  "nbformat_minor": 4
 }