// Numbas version: finer_feedback_settings
{"name": "Matrix multiplication", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": ["checked2015", "linear algebra", "mas104220122013CBA4_2", "MAS1602", "MAS2223", "matrices", "matrix", "matrix manipulation", "matrix multiplication", "multiply matrix", "products of matrices"], "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", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "gaps": [{"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{p1}", "maxValue": "{p1}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{p2}", "maxValue": "{p2}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{p3}", "maxValue": "{p3}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{q1}", "maxValue": "{q1}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{q2}", "maxValue": "{q2}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{q3}", "maxValue": "{q3}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ba11}", "maxValue": "{ba11}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ba12}", "maxValue": "{ba12}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ba13}", "maxValue": "{ba13}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ba21}", "maxValue": "{ba21}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ba22}", "maxValue": "{ba22}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ba23}", "maxValue": "{ba23}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ba31}", "maxValue": "{ba31}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ba32}", "maxValue": "{ba32}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ba33}", "maxValue": "{ba33}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ab11}", "maxValue": "{ab11}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ab12}", "maxValue": "{ab12}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ab13}", "maxValue": "{ab13}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ab21}", "maxValue": "{ab21}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ab22}", "maxValue": "{ab22}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ab23}", "maxValue": "{ab23}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ab31}", "maxValue": "{ab31}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ab32}", "maxValue": "{ab32}", "allowFractions": false, "correctAnswerFraction": false}, {"scripts": {}, "showPrecisionHint": false, "type": "numberentry", "showCorrectAnswer": true, "marks": 0.5, "minValue": "{ab33}", "maxValue": "{ab33}", "allowFractions": false, "correctAnswerFraction": false}]}, {"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", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "gaps": [{"maxAnswers": 0, "scripts": {}, "shuffleChoices": true, "answers": ["<strong>Can be calculated</strong>", "<strong>Cannot be calculated</strong>"], "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>"], "showCorrectAnswer": true, "marks": 0, "shuffleAnswers": false, "matrix": "v", "maxMarks": 0, "minMarks": 0, "layout": {"expression": ""}, "minAnswers": 0, "type": "m_n_x"}]}], "preamble": {"js": "", "css": ""}, "functions": {}, "advice": "", "metadata": {"description": "<p>Elementary Exercises in multiplying matrices.&nbsp;</p>", "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"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>Answer the following questions on matrices.</p>\n    <p>&nbsp;</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "name": "Matrix multiplication", "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "showQuestionGroupNames": false, "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"], "variables": {"z": {"name": "z", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-2,-1,1,2)"}, "w": {"name": "w", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(3..5)"}, "y": {"name": "y", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "u+random(0,z)"}, "ba33": {"name": "ba33", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": 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