// Numbas version: exam_results_page_options
{"name": "Multiply 2x2 matrices", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "matrix([ [random(-3,-1,0,3),random(-3..1)], [random(2,3),random(-3..-1)] ])", "description": "", "name": "b"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "matrix([ [random(-2,1,2),random(1..4)], [random(-2..2),random(1..3)] ])", "description": "", "name": "a"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "matrix([ [random(1,0,4), a[0][1]+b[0][1]], [random(2..5),random(0,1)] ])", "description": "", "name": "c"}}, "ungrouped_variables": ["a", "b", "c"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Multiply 2x2 matrices", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"allowFractions": false, "correctAnswer": "a*b", "markPerCell": false, "allowResize": false, "correctAnswerFractions": false, "numRows": "2", "scripts": {}, "type": "matrix", "numColumns": "2", "tolerance": 0, "showCorrectAnswer": true, "marks": 1}], "type": "gapfill", "prompt": "<p style=\"text-align: center;\">$\\mathbf{AB} = \\var{A}\\var{B} = $&nbsp;[[0]]</p>", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"allowFractions": false, "correctAnswer": "b*a", "markPerCell": false, "allowResize": false, "correctAnswerFractions": false, "numRows": "2", "scripts": {}, "type": "matrix", "numColumns": "2", "tolerance": 0, "showCorrectAnswer": true, "marks": 1}], "type": "gapfill", "prompt": "<p style=\"text-align: center;\">$\\mathbf{BA} = \\var{B}\\var{A} = $&nbsp;[[0]]</p>", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"allowFractions": false, "correctAnswer": "c*b", "markPerCell": false, "allowResize": false, "correctAnswerFractions": false, "numRows": "2", "scripts": {}, "type": "matrix", "numColumns": "2", "tolerance": 0, "showCorrectAnswer": true, "marks": 1}], "type": "gapfill", "prompt": "<p style=\"text-align: center;\">$\\mathbf{CB} = \\var{C}\\var{B} = $&nbsp;[[0]]</p>", "showCorrectAnswer": true, "marks": 0}, {"scripts": {}, "gaps": [{"allowFractions": false, "correctAnswer": "a*c", "markPerCell": false, "allowResize": false, "correctAnswerFractions": false, "numRows": "2", "scripts": {}, "type": "matrix", "numColumns": "2", "tolerance": 0, "showCorrectAnswer": true, "marks": 1}], "type": "gapfill", "prompt": "<p style=\"text-align: center;\">$\\mathbf{AC} = \\var{A}\\var{C} = $&nbsp;[[0]]</p>", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>Let</p>\n<p>\\begin{align} \\mathbf{A} &amp;= \\var{a}, &amp; \\mathbf{B} &amp;= \\var{b}, &amp; \\mathbf{C} &amp;= \\var{c} \\end{align}</p>\n<p>Calculate the following products of these matrices:</p>", "tags": ["checked2015", "MAS1602", "matrices", "matrix", "matrix multiplication", "matrix product", "multiplication of matrices", "multiplying matrices", "product of matrices", "tested1"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>10/07/2012:</strong></p>\n        <p>Added tags.</p>\n        <p>Display of matrices looks untidy when individual components include negative numbers.</p>\n        <p>Is it worthwhile restricting all components of matrices to be non zero?</p>\n        <p>Question appears to be working correctly.</p>\n        <p><strong>24/12/2012:</strong></p>\n        <p>Checked calculations, OK. Added tested1 tag.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Multiplication of $2 \\times 2$ matrices.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<h4>a)</h4>\n<p>\\begin{align}<br/>\\mathbf{AB} &amp;= \\var{A}\\var{B} \\\\<br/>&amp;= \\begin{pmatrix} \\simplify[]{ {a[0][0]}*{b[0][0]}+{a[0][1]}*{b[1][0]} } &amp; \\simplify[]{ {a[0][0]}*{b[0][1]} + {a[0][1]}*{b[1][1]} } \\\\ \\simplify[]{ {a[1][0]}*{b[0][0]} + {a[1][1]}*{b[1][0]} } &amp; \\simplify[]{ {a[1][0]}*{b[0][1]} + {a[1][1]}*{b[1][1]} } \\end{pmatrix} \\\\<br/>&amp;= \\var{a*b}<br/>\\end{align}</p>\n<h4>b)</h4>\n<p>\\begin{align}<br/>\\mathbf{BA} &amp;= \\var{B}\\var{A} \\\\<br/>&amp;= \\begin{pmatrix} \\simplify[]{ {b[0][0]}*{a[0][0]}+{b[0][1]}*{a[1][0]} } &amp; \\simplify[]{ {b[0][0]}*{a[0][1]} + {b[0][1]}*{a[1][1]} } \\\\ \\simplify[]{ {b[1][0]}*{a[0][0]} + {b[1][1]}*{a[1][0]} } &amp; \\simplify[]{ {b[1][0]}*{a[0][1]} + {b[1][1]}*{a[1][1]} } \\end{pmatrix} \\\\<br/>&amp;= \\var{b*a}<br/>\\end{align}</p>\n<h4>c)</h4>\n<p>\\begin{align}<br/>\\mathbf{CB} &amp;= \\var{C}\\var{B} \\\\<br/>&amp;= \\begin{pmatrix} \\simplify[]{ {c[0][0]}*{b[0][0]}+{c[0][1]}*{b[1][0]} } &amp; \\simplify[]{ {c[0][0]}*{b[0][1]} + {c[0][1]}*{b[1][1]} } \\\\ \\simplify[]{ {c[1][0]}*{b[0][0]} + {c[1][1]}*{b[1][0]} } &amp; \\simplify[]{ {c[1][0]}*{b[0][1]} + {c[1][1]}*{b[1][1]} } \\end{pmatrix} \\\\<br/>&amp;= \\var{c*b}<br/>\\end{align}</p>\n<h4>d)</h4>\n<p>\\begin{align}<br/>\\mathbf{AC} &amp;= \\var{A}\\var{C} \\\\<br/>&amp;= \\begin{pmatrix} \\simplify[]{ {a[0][0]}*{c[0][0]}+{a[0][1]}*{c[1][0]} } &amp; \\simplify[]{ {a[0][0]}*{c[0][1]} + {a[0][1]}*{c[1][1]} } \\\\ \\simplify[]{ {a[1][0]}*{c[0][0]} + {a[1][1]}*{c[1][0]} } &amp; \\simplify[]{ {a[1][0]}*{c[0][1]} + {a[1][1]}*{c[1][1]} } \\end{pmatrix} \\\\<br/>&amp;= \\var{a*c}<br/>\\end{align}</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}