// Numbas version: finer_feedback_settings
{"name": "Maria's copy of  Introduction to Matrices", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": [], "tags": [], "metadata": {"description": "<p>a<sub>ij<sup>&nbsp; notation and definition of the order of a matrix.</sup></sub></p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "extensions": [], "statement": "<p>Matrices are rectangular arrays of numbers arranged in rows and columns. &nbsp;For example</p>\n<p>$\\begin{pmatrix} 1&amp;2\\\\ 4&amp;5\\\\ \\end{pmatrix} , &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;\\begin{pmatrix} 0&amp;-1\\ &amp;3\\\\2&amp;4&amp;-2 \\end{pmatrix}$</p>\n<p>The rows run across the matrices while the columns run down the matrices. &nbsp;Thus in the first matrix above the numbers $\\begin{pmatrix}1&amp;2\\end{pmatrix}$ are in the first row while the numbers $\\begin{pmatrix}4&amp;5\\end{pmatrix}$ are in the second row and similarly the numbers $\\begin{pmatrix} 1\\\\ 4\\\\ \\end{pmatrix}$&nbsp;are in the first column while the numbers $\\begin{pmatrix} 2\\\\ 5\\\\ \\end{pmatrix}$&nbsp;are in the second column.</p>\n<p>A matrix with $\\bf&nbsp;m$ rows and $\\bf n$<strong>&nbsp;</strong>columns is called a matrix of <em>order</em> $\\bf&nbsp;m\\times n$ or <em>dimension</em> $\\bf m\\times&nbsp;n$&nbsp;(or an $\\bf m\\times&nbsp;n$ matrix for&nbsp;brevity).</p>\n<p>When working with matrices the positions of the numbers in the arrays are as important as the actual values of the numbers. &nbsp;Given a matrix called &nbsp;$A$<strong>&nbsp;</strong>the number in row $i$ and column $j$ is usually denoted $a_{ij}$ it is also sometimes called the $ij^{th}$ element of the matrix $A$.</p>", "advice": "<p>a) &nbsp; &nbsp;&nbsp; Remember that the dimensions are $\\rm \\color{red}{rows} \\times \\color{blue}{columns}$, so you need to count the number or rwos and columns in the matrix and wrtite them in that order.</p>\n<p>b) &nbsp; &nbsp;&nbsp; Remember that the elements are in the form $A_{\\rm \\color{red}{ rows},\\color{blue}{columns}}$ where $A$ is the matrix.</p>\n<p>For example if we are looking for $a_{12}$ we look at the matrix $A= \\begin{pmatrix} \\var{a11} &amp;\\bf( \\underline{\\var{a12}}) \\\\ \\var{a21} &amp; \\var{a22}\\end{pmatrix}$ we want the the element on $\\rm \\color{red}{row ~ 1}$ and $\\rm \\color{blue}{column ~ 2}$ which in this case is $\\bf \\underline{\\var{a12}}$</p>\n<p></p>", "parts": [{"prompt": "<p><strong>Example 1 -- </strong>Give the dimensions of the following matrices:</p>\n<p>$A=\\var{A}$ has dimensions [[0]]$ \\times $[[1]]</p>\n<p>$B=\\var{B}$ is a [[2]]$ \\times$[[3]] matrix</p>\n<p>$C=\\var{C}$ is of dimension [[4]]$ \\times$[[5]]</p>", 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"scripts": {}, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "maxValue": "{n2}", "variableReplacements": []}, {"allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "type": "numberentry", "correctAnswerFraction": false, "minValue": "{m2}", "scripts": {}, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "maxValue": "{m2}", "variableReplacements": []}, {"allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "type": "numberentry", "correctAnswerFraction": false, "minValue": "{n3}", "scripts": {}, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "maxValue": "{n3}", "variableReplacements": []}, {"allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "type": "numberentry", "correctAnswerFraction": false, "minValue": "{m3}", "scripts": {}, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "maxValue": "{m3}", "variableReplacements": []}]}, {"prompt": "<p><strong>Example 2 -- </strong>Give the values of the following elements of the matrices from example 1 above:</p>\n<p>$a_{\\var{n1}\\var{m1}}=$[[0]]</p>\n<p>$b_{\\var{n2}\\var{m2}}=$[[1]]</p>\n<p>$c_{\\var{n3}\\var{m3}}=$[[2]]</p>\n<p>$c_{\\var{n4}\\var{m4}}=$[[3]]</p>", "variableReplacementStrategy": "originalfirst", "marks": 0, "showCorrectAnswer": true, "type": "gapfill", "scripts": {}, "variableReplacements": [], "gaps": [{"allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "type": "numberentry", "correctAnswerFraction": false, "minValue": "A[n1-1][m1-1]", "scripts": {}, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "maxValue": "A[n1-1][m1-1]", "variableReplacements": []}, {"allowFractions": false, "notationStyles": ["plain", "en", "si-en"], "marks": 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