// Numbas version: finer_feedback_settings
{"name": "John's copy of Matrix multiplication", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"js": "", "css": ""}, "name": "John's copy of Matrix multiplication", "ungrouped_variables": ["ba21", "a21", "a22", "a23", "b23", "b22", "b21", "ba22", "w3", "w2", "w1", "ba11", "a11", "ba13", "p1", "q1", "q", "q3", "q2", "ab23", "ab22", "ab21", "s3", "s2", "s1", "a12", "s7", "s6", "s5", "s4", "b12", "b13", "b11", "c13", "c12", "c11", "a33", "a32", "a31", "ba32", "ba33", "a13", "ba31", "s10", "s9", "b32", "b31", "v1", "v2", "v3", "mae", "mad", "mag", "mah", "ba12", "b33", "p2", "p3", "ba23", "ab11", "ab31", "ab32", "ab33", "ab12", "m", "s8", "n", "mac", "p", "s", "r", "u", "w", "v", "y", "x", "z", "ab13"], "showQuestionGroupNames": false, "metadata": {"notes": "\n                                                            \t\t                            \t\t<p><strong>5/07/2012:</strong></p>\n                                                            \t\t                            \t\t<p>Added tags.</p>\n                                                            \t\t                            \t\t<p>Question appears to be working correctly.</p>\n                                                            \t\t                            \t\t<p>&nbsp;</p>\n                                                            \t\t                            \n                                                            \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Elementary Exercises in multiplying matrices.&nbsp;</p>"}, "parts": [{"prompt": "\n      \n      \n      <p>Let</p>\n      \n      \n      \n      <p>\\[A = \\left(\\begin{array}{rrr} \\var{a11} &#38; \\var{a12} &#38; \\var{a13}\\\\ \\var{a21} &#38; \\var{a22} &#38; \\var{a23}\\\\ \\var{a31} &#38; \\var{a32} &#38; \\var{a33}\\\\\n      \n      \\end{array}\\right),\\;\\;\\;\\;\n      \n      B=  \\left(\\begin{array}{rrr} \\var{b11} &#38; \\var{b12} &#38; \\var{b13}\\\\ \\var{b21} &#38; \\var{b22} &#38; \\var{b23}\\\\ \\var{b31} &#38; \\var{b32} &#38; \\var{b33}\\\\\n      \n      \\end{array}\\right),\\;\\;\\;\\;\n      \n      v= \\left(\\begin{array}{r} \\var{v1}\\\\ \\var{v2} \\\\ \\var{v3} \\end{array}\\right),\\;\\;\\;\\;\n      \n      w= \\left(\\begin{array}{r} \\var{w1}\\\\ \\var{w2} \\\\ \\var{w3} \\end{array}\\right)\\]</p>\n      \n      \n      \n      <p>Find the following products:</p>\n      \n      \n      \n      <table>\n      \n      <tr>\n      \n      <td rowspan=\"3\">\\[ Av=\\left( \\begin{matrix}  \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n      \n      <td> [[0]] </td>\n      \n      <td rowspan=\"3\">\\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\  \\end{matrix} \\right.\\] </td>\n      \n      </tr>\n      \n      <tr>\n      \n      <td> [[1]] </td>\n      \n      </tr>\n      \n      <tr>\n      \n      <td> [[2]] </td>\n      \n      </tr>\n      \n      <tr>\n      \n      <td rowspan=\"3\">\\[ Bw=\\left( \\begin{matrix}  \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n      \n      <td> [[3]] </td>\n      \n      <td rowspan=\"3\">\\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\  \\end{matrix} \\right.\\] </td>\n      \n      </tr>\n      \n      <tr>\n      \n      <td> [[4]] </td>\n      \n      </tr>\n      \n      <tr>\n      \n      <td> [[5]] </td>\n      \n      </tr>\n      \n      </table>\n      \n      \n      \n      <table>\n      \n      <tr>\n      \n      <td rowspan=\"3\">\\[BA=\\left( \\begin{matrix}  \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n      \n      <td> [[6]] </td>\n      \n      <td> [[7]] </td>\n      \n      <td> [[8]]  </td>\n      \n      <td rowspan=\"3\">\\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\  \\end{matrix} \\right.\\] </td>\n      \n      </tr>\n      \n      <tr>\n      \n      <td> [[9]] </td>\n      \n      <td> [[10]] </td>\n      \n      <td> [[11]] </td>\n      \n      </tr>\n      \n      <tr>\n      \n      <td> [[12]] </td>\n      \n      <td> [[13]] </td>\n      \n      <td> [[14]] </td>\n      \n      </tr>\n      \n      </table>\n      \n      \n      \n      <table>\n      \n      <tr>\n      \n      <td rowspan=\"3\">\\[AB=\\left( \\begin{matrix}  \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n      \n      <td> [[15]] </td>\n      \n      <td> [[16]] </td>\n      \n      <td> [[17]]  </td>\n      \n      <td rowspan=\"3\">\\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\  \\end{matrix} \\right.\\] </td>\n      \n      </tr>\n      \n      <tr>\n      \n      <td> [[18]] </td>\n      \n      <td> [[19]] </td>\n      \n      <td> [[20]] </td>\n      \n      </tr>\n      \n      <tr>\n      \n      <td> [[21]] </td>\n      \n      <td> [[22]] </td>\n      \n      <td> [[23]] </td>\n      \n      </tr>\n      \n      </table>\n      \n      \n        \n      ", "type": "gapfill", "gaps": [{"minValue": "{p1}", "maxValue": "{p1}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{p2}", "maxValue": "{p2}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{p3}", "maxValue": "{p3}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{q1}", "maxValue": "{q1}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{q2}", "maxValue": "{q2}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{q3}", "maxValue": "{q3}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ba11}", "maxValue": "{ba11}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ba12}", "maxValue": "{ba12}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ba13}", "maxValue": "{ba13}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ba21}", "maxValue": "{ba21}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ba22}", "maxValue": "{ba22}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ba23}", "maxValue": "{ba23}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ba31}", "maxValue": "{ba31}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ba32}", "maxValue": "{ba32}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ba33}", "maxValue": "{ba33}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ab11}", "maxValue": "{ab11}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ab12}", "maxValue": "{ab12}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ab13}", "maxValue": "{ab13}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ab21}", "maxValue": "{ab21}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ab22}", "maxValue": "{ab22}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ab23}", "maxValue": "{ab23}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ab31}", "maxValue": "{ab31}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ab32}", "maxValue": "{ab32}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}, {"minValue": "{ab33}", "maxValue": "{ab33}", "correctAnswerFraction": false, "allowFractions": false, "marks": 0.5, "showPrecisionHint": false, "scripts": {}, "showCorrectAnswer": true, "type": "numberentry"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true}, {"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>", "type": "gapfill", "gaps": [{"layout": {"expression": ""}, "scripts": {}, "showCorrectAnswer": true, "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "matrix": "v", "type": "m_n_x", "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>"], "answers": ["<strong>Can be calculated</strong>", "<strong>Cannot be calculated</strong>"], "marks": 0, "maxAnswers": 0, "shuffleAnswers": false, "shuffleChoices": true}], "marks": 0, "scripts": {}, "showCorrectAnswer": true}], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "statement": "<p>Answer the following questions on matrices.</p>\n    <p>&nbsp;</p>", "type": "question", "variable_groups": [], "advice": "", "functions": {}, "variables": {"mad": {"group": "Ungrouped variables", "name": "mad", "definition": "matrix(repeat(repeat(random(-2..9),q),p))", "templateType": "anything", "description": ""}, "b21": {"group": "Ungrouped variables", "name": "b21", "definition": "random(0..2)", "templateType": "anything", "description": ""}, "s6": {"group": "Ungrouped variables", "name": "s6", "definition": "if(r=3,0.5,-0.5)", "templateType": "anything", "description": ""}, "s7": {"group": "Ungrouped variables", "name": "s7", "definition": "if(u=y,0.5,-0.5)", "templateType": "anything", "description": ""}, "s8": {"group": "Ungrouped variables", "name": "s8", "definition": "if(x=r,0.5,-0.5)", "templateType": "anything", "description": ""}, "a12": {"group": "Ungrouped variables", "name": "a12", "definition": "random(-1,1,2)", "templateType": "anything", "description": ""}, "y": {"group": "Ungrouped variables", "name": "y", "definition": "u+random(0,z)", "templateType": "anything", "description": ""}, "ab21": {"group": "Ungrouped variables", "name": "ab21", "definition": "a21*b11+a22*b21+a23*b31", "templateType": "anything", "description": ""}, "q3": {"group": "Ungrouped variables", "name": "q3", "definition": "b31*w1+b32*w2+b33*w3", "templateType": "anything", "description": ""}, "c12": {"group": "Ungrouped variables", "name": "c12", "definition": "random(1..3)", "templateType": "anything", "description": ""}, "mac": {"group": "Ungrouped variables", "name": "mac", "definition": "matrix(repeat(repeat(random(-2..9),n),m))", "templateType": "anything", "description": ""}, "b13": {"group": "Ungrouped variables", "name": "b13", "definition": "random(-2..2)", "templateType": "anything", "description": ""}, "ab13": {"group": "Ungrouped variables", "name": "ab13", "definition": "a11*b13+a12*b23+a13*b33", "templateType": "anything", "description": ""}, "z": {"group": "Ungrouped variables", "name": "z", "definition": "random(-2,-1,1,2)", "templateType": "anything", "description": ""}, "s2": {"group": "Ungrouped variables", "name": "s2", "definition": "if(q=m,0.5,-0.5)", "templateType": "anything", "description": ""}, "s5": {"group": "Ungrouped variables", "name": "s5", "definition": "if(m=3,0.5,-0.5)", "templateType": "anything", "description": ""}, "b32": {"group": "Ungrouped variables", "name": "b32", "definition": "random(-3..3)", "templateType": "anything", "description": ""}, "ba23": {"group": "Ungrouped variables", "name": "ba23", "definition": "b21*a13+b22*a23+b23*a33", "templateType": "anything", "description": ""}, "ba21": {"group": "Ungrouped variables", "name": "ba21", "definition": "b21*a11+b22*a21+b23*a31", "templateType": "anything", "description": ""}, "ab31": {"group": "Ungrouped variables", "name": "ab31", "definition": "a31*b11+a32*b21+a33*b31", "templateType": "anything", "description": ""}, "a13": {"group": "Ungrouped variables", "name": "a13", "definition": "random(1..2)", "templateType": "anything", "description": ""}, "p2": {"group": "Ungrouped variables", "name": "p2", "definition": "a21*v1+a22*v2+a23*v3", "templateType": "anything", "description": ""}, "ab12": {"group": "Ungrouped variables", "name": "ab12", "definition": "a11*b12+a12*b22+a13*b32", "templateType": "anything", "description": ""}, "b11": {"group": "Ungrouped variables", "name": "b11", "definition": "random(0,1)", "templateType": "anything", "description": ""}, "q": {"group": "Ungrouped variables", "name": "q", "definition": "m+random(0,z)", "templateType": "anything", "description": ""}, "c11": {"group": "Ungrouped variables", "name": "c11", "definition": "random(-2..2)", "templateType": "anything", "description": ""}, "w1": {"group": "Ungrouped variables", "name": "w1", "definition": "random(4..6)", "templateType": "anything", "description": ""}, "q1": {"group": "Ungrouped variables", "name": "q1", "definition": "b11*w1+b12*w2+b13*w3", "templateType": "anything", "description": ""}, "mag": {"group": "Ungrouped variables", "name": "mag", "definition": "matrix(repeat(repeat(random(-2..9),u),w))", "templateType": "anything", "description": ""}, "ab32": {"group": "Ungrouped variables", "name": "ab32", "definition": "a31*b12+a32*b22+a33*b32", "templateType": "anything", "description": ""}, "q2": {"group": "Ungrouped variables", "name": "q2", "definition": "b21*w1+b22*w2+b23*w3", "templateType": "anything", "description": ""}, "s3": {"group": "Ungrouped variables", "name": "s3", "definition": "if(s=5,0.5,-0.5)", "templateType": "anything", "description": ""}, "s4": {"group": "Ungrouped variables", "name": "s4", "definition": "if(r=2,0.5,-0.5)", "templateType": "anything", "description": ""}, "p": {"group": "Ungrouped variables", "name": "p", "definition": "n+random(0,z)", "templateType": "anything", "description": ""}, "ba31": {"group": "Ungrouped variables", "name": "ba31", "definition": "b31*a11+b32*a21+b33*a31", "templateType": "anything", "description": ""}, "ab33": {"group": "Ungrouped variables", "name": "ab33", "definition": "a31*b13+a32*b23+a33*b33", "templateType": "anything", "description": ""}, "p1": {"group": "Ungrouped variables", "name": "p1", "definition": "a11*v1+a12*v2+a13*v3", "templateType": "anything", "description": ""}, "v1": {"group": "Ungrouped variables", "name": "v1", "definition": "random(-3..3)", "templateType": "anything", "description": ""}, "ab23": {"group": "Ungrouped variables", "name": "ab23", "definition": "a21*b13+a22*b23+a23*b33", "templateType": "anything", "description": ""}, "a32": {"group": "Ungrouped variables", "name": "a32", "definition": "random(-4..4)", "templateType": "anything", "description": ""}, "m": {"group": "Ungrouped variables", "name": "m", "definition": "random(3..4)", "templateType": "anything", "description": ""}, "v": {"group": "Ungrouped variables", "name": "v", "definition": "[[s1,-s1],[s2,-s2],[s3,-s3],[s4,-s4],[s5,-s5],[s6,-s6],[s7,-s7],[s8,-s8],[s9,-s9],[s10,-s10]]", "templateType": "anything", "description": ""}, "a31": {"group": "Ungrouped variables", "name": "a31", "definition": "random(1..3)", "templateType": "anything", "description": ""}, "ba22": {"group": "Ungrouped variables", "name": "ba22", "definition": "b21*a12+b22*a22+b23*a32", "templateType": "anything", "description": ""}, "s": {"group": "Ungrouped variables", "name": "s", "definition": "random(4..6)", "templateType": "anything", "description": ""}, "a11": {"group": "Ungrouped variables", "name": "a11", "definition": "random(1..4)", "templateType": "anything", "description": ""}, "p3": {"group": "Ungrouped variables", "name": "p3", "definition": "a31*v1+a32*v2+a33*v3", "templateType": "anything", "description": ""}, "a33": {"group": "Ungrouped variables", "name": "a33", "definition": "random(1..4)", "templateType": "anything", "description": ""}, "mah": {"group": "Ungrouped variables", "name": "mah", "definition": "matrix(repeat(repeat(random(-2..9),x),y))", "templateType": "anything", "description": ""}, "b31": {"group": "Ungrouped variables", "name": "b31", "definition": "random(1..3)", "templateType": "anything", "description": ""}, "ab11": {"group": "Ungrouped variables", "name": "ab11", "definition": "a11*b11+a12*b21+a13*b31", "templateType": "anything", "description": ""}, "u": {"group": "Ungrouped variables", "name": "u", "definition": "random(3..4)", "templateType": "anything", "description": ""}, "a23": {"group": "Ungrouped variables", "name": "a23", "definition": "random(-2..2)", "templateType": "anything", "description": ""}, "s9": {"group": "Ungrouped variables", "name": "s9", "definition": "if(w=3,0.5,-0.5)", "templateType": "anything", "description": ""}, "c13": {"group": "Ungrouped variables", "name": "c13", "definition": "random(1..2)", "templateType": "anything", "description": ""}, "a21": {"group": "Ungrouped variables", "name": "a21", "definition": "random(-1,0,1)", "templateType": "anything", "description": ""}, "w2": {"group": "Ungrouped variables", "name": "w2", "definition": "random(-4..4)", "templateType": "anything", "description": ""}, "n": {"group": "Ungrouped variables", "name": "n", "definition": "random(3..6 except m)", "templateType": "anything", "description": ""}, "x": {"group": "Ungrouped variables", "name": "x", "definition": "u+random(0,z)", "templateType": "anything", "description": ""}, "ab22": {"group": "Ungrouped variables", "name": "ab22", "definition": "a21*b12+a22*b22+a23*b32", "templateType": "anything", "description": ""}, "ba13": {"group": "Ungrouped variables", "name": "ba13", "definition": "b11*a13+b12*a23+b13*a33", "templateType": "anything", "description": ""}, "w3": {"group": "Ungrouped variables", "name": "w3", "definition": "random(-4..4)", "templateType": "anything", "description": ""}, "a22": {"group": "Ungrouped variables", "name": "a22", "definition": "random(-4,-3,-2,-1,1,2,3,5)", "templateType": "anything", "description": ""}, "mae": {"group": "Ungrouped variables", "name": "mae", "definition": "matrix(repeat(repeat(random(-2..9),s),r))", "templateType": "anything", "description": ""}, "v2": {"group": "Ungrouped variables", "name": "v2", "definition": "random(1..4)", "templateType": 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