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"showCorrectAnswer": true, "allowResize": false, "useCustomName": false, "numColumns": "3", "scripts": {}, "tolerance": 0, "allowFractions": false, "markPerCell": false, "customName": ""}, {"adaptiveMarkingPenalty": 0, "marks": 1, "correctAnswer": "matrix([\n    [ab11,ab12,ab13],\n    [ab21,ab22,ab23],\n    [ab31,ab32,ab33]\n])", "customMarkingAlgorithm": "", "showFeedbackIcon": true, "variableReplacements": [], "numRows": "3", "type": "matrix", "correctAnswerFractions": false, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "allowResize": false, "useCustomName": false, "numColumns": "3", "scripts": {}, "tolerance": 0, "allowFractions": false, "markPerCell": false, "customName": ""}], "showCorrectAnswer": true, "customName": "", "sortAnswers": false, "useCustomName": false, "scripts": {}, "prompt": "<p>Let</p>\n<p>\\[A = \\left(\\begin{array}{rrr} \\var{a11} &amp; \\var{a12} &amp; \\var{a13}\\\\ \\var{a21} &amp; \\var{a22} &amp; \\var{a23}\\\\ \\var{a31} &amp; \\var{a32} &amp; \\var{a33}\\\\ \\end{array}\\right),\\;\\;\\;\\; B= \\left(\\begin{array}{rrr} \\var{b11} &amp; \\var{b12} &amp; \\var{b13}\\\\ \\var{b21} &amp; \\var{b22} &amp; \\var{b23}\\\\ \\var{b31} &amp; \\var{b32} &amp; \\var{b33}\\\\ \\end{array}\\right),\\;\\;\\;\\; v= \\left(\\begin{array}{r} \\var{v1}\\\\ \\var{v2} \\\\ \\var{v3} \\end{array}\\right),\\;\\;\\;\\; w= \\left(\\begin{array}{r} \\var{w1}\\\\ \\var{w2} \\\\ \\var{w3} \\end{array}\\right)\\]</p>\n<p>Find the following products:</p>\n<p>$Av = $ [[0]]</p>\n<p>$Bw = $ [[1]]</p>\n<p>$BA = $ [[2]]</p>\n<p>$AB = $ [[3]]</p>", "variableReplacementStrategy": "originalfirst"}, {"adaptiveMarkingPenalty": 0, "marks": 0, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "variableReplacements": [], "type": "gapfill", "extendBaseMarkingAlgorithm": true, "unitTests": [], "gaps": [{"showFeedbackIcon": true, "type": "m_n_x", "showCellAnswerState": true, "extendBaseMarkingAlgorithm": true, "maxMarks": 0, "minMarks": 0, "displayType": "radiogroup", "customName": "", "shuffleChoices": true, "scripts": {}, "customMarkingAlgorithm": "", "matrix": "v", "adaptiveMarkingPenalty": 0, "marks": 0, "choices": ["<p>$CD$</p>", "<p>$DC$</p>", "<p>$EF$</p>", "<p>$FE$</p>", "<p>$BC$</p>", "<p>$AE$</p>", "<p>$GH$</p>", "<p>$HE$</p>", "<p>$AG$</p>", "<p>$GB$</p>"], "variableReplacementStrategy": "originalfirst", "minAnswers": 0, "variableReplacements": [], "unitTests": [], "warningType": "none", "maxAnswers": 0, "useCustomName": false, "showCorrectAnswer": true, "shuffleAnswers": false, "answers": ["<strong>Can be calculated</strong>", "<strong>Cannot be calculated</strong>"], "layout": {"expression": ""}}], "showCorrectAnswer": true, "customName": "", "sortAnswers": false, "useCustomName": false, "scripts": {}, "prompt": "<p>Consider the following matrices together with the matrices from the first part of the question.</p>\n<p>\\[\\begin{eqnarray}&amp;C=&amp; \\var{mac},\\;\\;\\;\\; &amp;D=&amp; \\var{mad},\\;\\;\\; \\;&amp;E= &amp;\\var{mae}\\\\&amp;F=&amp; \\left(\\begin{array}{rr} \\var{w1} &amp; \\var{a12}\\\\ \\var{w2} &amp; \\var{b23} \\\\ \\var{w3} &amp; \\var{w2} \\\\\\var{v1} &amp; \\var{b12}\\\\ 0 &amp; \\var{-w2} \\end{array}\\right),\\;\\;\\;\\;&amp;G=&amp;\\var{mag},\\;\\;\\;\\;&amp;H=&amp;\\var{mah} \\end{eqnarray}\\]</p>\n<p>Which of the following products of matrices can be calculated?</p>\n<p>[[0]]</p>\n<p><strong>Please note that for every correct answer you get 0.5 marks and for every incorrect answer 0.5 is taken away. The minimum mark you can get is 0.</strong></p>", "variableReplacementStrategy": "originalfirst"}], "statement": "\n  <p>Answer the following questions on matrices.</p>\n  <p>&nbsp;</p>\n  ", "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}