// Numbas version: exam_results_page_options
{"name": "EG3101 EG5116 EG4103 Matrices: Multiplying two 3x3 matrices", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["matrices"], "name": "EG3101 EG5116 EG4103 Matrices: Multiplying two 3x3 matrices", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>Remember : matrix multiplication requires each row of the first matrix A be multiplied by each column of the second matrix B:</p>\n<p>If \\[&nbsp; A=\\left( \\begin{array}{ccc}<br/>a &amp; b &amp; c&nbsp; \\\\d&nbsp;&amp;&nbsp;e&nbsp;&amp; f\\\\g &amp; h &amp; j&nbsp;\\end{array} \\right),\\]</p>\n<p style=\"text-align: left;\">and \\[ B=\\left( \\begin{array}{ccc}<br/>k&nbsp;&amp; l &amp; m \\\\n &amp; p &amp; q\\\\r &amp; s&nbsp;&amp; t\\end{array} \\right)\\],</p>\n<p>then \\[ AB=\\left( \\begin{array}{ccc}<br/>ak+bn+cr &amp; al+bp+cs &amp;&nbsp;am+bq+ct&nbsp;&nbsp; \\\\dk+en+fr &amp; dl+ep+fs &amp;&nbsp;dm+eq+ft&nbsp;&nbsp; \\\\gk+hn+jr &amp; gl+hp+js &amp;&nbsp;gm+hq+jt&nbsp;&nbsp; <br/>\\end{array} \\right)\\]</p>\n<p></p>\n<p><span class=\"nb\">&nbsp;</span></p>\n<p><span class=\"nb\"><span class=\"k\"><span class=\"s\">&nbsp;</span></span></span></p>\n<p></p>", "rulesets": {}, "parts": [{"prompt": "<p>What is $\\simplify{{matrices[0]}*{matrices[1]}}$?</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"numRows": 1, "numColumns": 1, "allowResize": true, "allowFractions": false, "variableReplacements": [], "markPerCell": false, "variableReplacementStrategy": "originalfirst", "tolerance": 0, "correctAnswerFractions": false, "showCorrectAnswer": true, "correctAnswer": "matrices[0]*matrices[1]", "scripts": {}, "marks": 1, "type": "matrix"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p>You will possibly need to adjust the number of rows and the number of columns your solution requires by entering the correct values for your solution; the template will then alter to hold your solution.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"matrices": {"definition": "repeat(matrix(repeat(repeat(random(0..10)*random(1,1,1,-1),3),3)),3)", "templateType": "anything", "group": "Ungrouped variables", "name": "matrices", "description": "<p>A couple of random matrices to multiply together</p>"}}, "metadata": {"description": "<p>Multiplying two 3x3 matrices.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "bryan pearce", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/347/"}]}]}], "contributors": [{"name": "bryan pearce", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/347/"}]}