// Numbas version: exam_results_page_options
{"name": "Ch10 Q2", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "statement": "<p>Answer the following questions on matrices.</p>\n    <p>&nbsp;</p>", "extensions": ["stats"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "name": "Ch10 Q2", "parts": [{"marks": 0, "gaps": [{"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{p1}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{p1}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{p2}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{p2}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{p3}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{p3}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{q1}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{q1}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{q2}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{q2}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{q3}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{q3}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ba11}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ba11}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ba12}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ba12}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ba13}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ba13}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ba21}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ba21}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ba22}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ba22}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ba23}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ba23}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ba31}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ba31}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ba32}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ba32}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ba33}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ba33}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ab11}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ab11}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ab12}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ab12}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ab13}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ab13}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ab21}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ab21}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ab22}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ab22}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ab23}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ab23}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ab31}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ab31}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ab32}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ab32}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}, {"type": "numberentry", "showFeedbackIcon": true, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "allowFractions": false, "minValue": "{ab33}", "notationStyles": ["plain", "en", "si-en"], "marks": 0.5, "maxValue": "{ab33}", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}}], "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "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<table>\n<tbody>\n<tr>\n<td style=\"text-align: left;\" rowspan=\"3\">\\[ Av=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n<td>[[0]]</td>\n<td rowspan=\"3\">\\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n</tr>\n<tr>\n<td>[[1]]</td>\n</tr>\n<tr>\n<td>[[2]]</td>\n</tr>\n<tr>\n<td rowspan=\"3\">\\[ Bw=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n<td>[[3]]</td>\n<td rowspan=\"3\">\\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n</tr>\n<tr>\n<td>[[4]]</td>\n</tr>\n<tr>\n<td>[[5]]</td>\n</tr>\n</tbody>\n</table>\n<table style=\"width: 954px;\">\n<tbody>\n<tr>\n<td style=\"width: 372px;\" rowspan=\"3\">\\[BA=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n<td style=\"width: 45.13px;\">[[6]]</td>\n<td style=\"width: 48.86px;\">[[7]]</td>\n<td style=\"width: 47px;\">[[8]]</td>\n<td style=\"width: 359px;\" rowspan=\"3\">\\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n</tr>\n<tr>\n<td style=\"width: 45.13px;\">[[9]]</td>\n<td style=\"width: 48.86px;\">[[10]]</td>\n<td style=\"width: 47px;\">[[11]]</td>\n</tr>\n<tr>\n<td style=\"width: 45.13px;\">[[12]]</td>\n<td style=\"width: 48.86px;\">[[13]]</td>\n<td style=\"width: 47px;\">[[14]]</td>\n</tr>\n</tbody>\n</table>\n<table>\n<tbody>\n<tr>\n<td rowspan=\"3\">\\[AB=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n<td>[[15]]</td>\n<td>[[16]]</td>\n<td>[[17]]</td>\n<td rowspan=\"3\">\\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n</tr>\n<tr>\n<td>[[18]]</td>\n<td>[[19]]</td>\n<td>[[20]]</td>\n</tr>\n<tr>\n<td>[[21]]</td>\n<td>[[22]]</td>\n<td>[[23]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>"}], "variable_groups": [], "advice": "<p>When multiplying matrices you must do it such that:</p>\n<p style=\"text-align: center;\">$A=\\left (\\begin{matrix}a &amp; b &amp; c \\\\ d&amp;e&amp;f\\end{matrix} \\right) \\; \\; \\;B=\\left(\\begin{matrix}&nbsp; g\\\\&nbsp;h \\\\ i\\end{matrix}\\right)$</p>\n<p style=\"text-align: center;\">$\\Rightarrow \\; AB=\\left(\\begin{matrix}ag+bh+ci \\\\ dg+eh+fi \\end{matrix}\\right)$</p>\n<p style=\"text-align: left;\">Therefore:</p>\n<p style=\"text-align: center;\">$Av=\\left(\\begin{matrix} \\var{a11*v1}+\\var{a12*v2}+\\var{a13*v3} \\\\ \\var{a21*v1}+\\var{a22*v2}+\\var{a23*v3} \\\\ \\var{a31*v1}+\\var{a32*v2}+\\var{a33*v3}&nbsp;\\end{matrix} \\right)$</p>\n<p style=\"text-align: center;\">$\\Rightarrow \\left(\\begin{matrix} \\simplify{{a11*v1}+{a12*v2}+{a13*v3}} \\\\ \\simplify{{a21*v1}+{a22*v2}+{a23*v3}} \\\\ \\simplify{{a31*v1}+{a32*v2}+{a33*v3}}&nbsp;\\end{matrix} \\right)$</p>\n<p style=\"text-align: center;\">$\\\\ $</p>\n<p style=\"text-align: center;\">$Bw=\\left(\\begin{matrix} \\var{b11*w1}+\\var{b12*w2}+\\var{b13*w3} \\\\ \\var{b21*w1}+\\var{b22*w2}+\\var{b23*w3} \\\\ \\var{b31*w1}+\\var{b32*w2}+\\var{b33*w3}&nbsp;\\end{matrix} \\right)$</p>\n<p style=\"text-align: center;\">$\\Rightarrow \\left(\\begin{matrix} \\simplify{{b11*w1}+{b12*w2}+{b13*w3}} \\\\ \\simplify{{b21*w1}+{b22*w2}+{b23*w3}} \\\\ \\simplify{{b31*w1}+{b32*w2}+{b33*w3}}&nbsp;\\end{matrix} \\right)$</p>\n<p style=\"text-align: center;\">$\\\\ $</p>\n<p style=\"text-align: center;\">$BA=\\left(\\begin{matrix} \\var{b11*a11}+\\var{b12*a21}+\\var{b13*a31} &amp; \\var{b11*a12}+\\var{b12 a22}+\\var{b13 a32} &amp; \\var{b11 a13}+\\var{b12 a23}+\\var{b13 a33} \\\\&nbsp;\\var{b21*a11}+\\var{b22*a21}+\\var{b23*a31} &amp; \\var{b21*a12}+\\var{b22 a22}+\\var{b23 a32} &amp; \\var{b21 a13}+\\var{b22 a23}+\\var{b23 a33} \\\\ \\var{b31*a11}+\\var{b32*a21}+\\var{b33*a31} &amp; \\var{b31*a12}+\\var{b32 a22}+\\var{b33 a32} &amp; \\var{b31 a13}+\\var{b32 a23}+\\var{b33 a33} &nbsp;&nbsp;\\end{matrix}\\right)$</p>\n<p style=\"text-align: center;\">$\\Rightarrow \\left(\\begin{matrix} \\simplify{{b11*a11}+{b12*a21}+{b13*a31}} &amp; \\simplify{{b11*a12}+{b12 a22}+{b13 a32}} &amp; \\simplify{{b11 a13}+{b12 a23}+{b13 a33}} \\\\&nbsp;\\simplify{{b21*a11}+{b22*a21}+{b23*a31}} &amp; \\simplify{{b21*a12}+{b22 a22}+{b23 a32}} &amp; \\simplify{{b21 a13}+{b22 a23}+{b23 a33}} \\\\ \\simplify{{b31*a11}+{b32*a21}+{b33*a31}} &amp; \\simplify{{b31*a12}+{b32 a22}+{b33 a32}} &amp; \\simplify{{b31 a13}+{b32 a23}+{b33 a33}} &nbsp;&nbsp;\\end{matrix}\\right)$</p>\n<p style=\"text-align: center;\">$\\\\ $</p>\n<p style=\"text-align: center;\">$AB=\\left(\\begin{matrix} \\var{a11*b11}+\\var{a12*b21}+\\var{a13*b31} &amp; \\var{a11*b12}+\\var{a12 b22}+\\var{a13 b32} &amp; \\var{a11 b13}+\\var{a12 b23}+\\var{a13 b33} \\\\&nbsp;\\var{a21*b11}+\\var{a22*b21}+\\var{a23*b31} &amp; \\var{a21*b12}+\\var{a22 b22}+\\var{a23 b32} &amp; \\var{a21 b13}+\\var{a22 b23}+\\var{a23 b33} \\\\ \\var{a31*b11}+\\var{a32*b21}+\\var{a33*b31} &amp; \\var{a31*b12}+\\var{a32 b22}+\\var{a33 b32} &amp; \\var{a31 b13}+\\var{a32 b23}+\\var{a33 b33} &nbsp;&nbsp;\\end{matrix}\\right)$</p>\n<p style=\"text-align: center;\">$\\Rightarrow \\left(\\begin{matrix} \\simplify{{a11*b11}+{a12*b21}+{a13*b31}} &amp; \\simplify{{a11*b12}+{a12 b22}+{a13 b32}} &amp; \\simplify{{a11 b13}+{a12 b23}+{a13 b33}} \\\\&nbsp;\\simplify{{a21*b11}+{a22*b21}+{a23*b31}} &amp; \\simplify{{a21*b12}+{a22 b22}+{a23 b32}} &amp; \\simplify{{a21 b13}+{a22 b23}+{a23 b33}} \\\\ \\simplify{{a31*b11}+{a32*b21}+{a33*b31}} &amp; \\simplify{{a31*b12}+{a32 b22}+{a33 b32}} &amp; \\simplify{{a31 b13}+{a32 b23}+{a33 b33}} &nbsp;&nbsp;\\end{matrix}\\right)$</p>\n<p style=\"text-align: center;\"></p>", "tags": [], "preamble": {"css": "", "js": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "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": {"ba31": {"name": "ba31", "description": "", "definition": "b31*a11+b32*a21+b33*a31", "templateType": "anything", "group": "Ungrouped variables"}, "c13": {"name": "c13", "description": "", "definition": "random(1..2)", "templateType": "anything", "group": "Ungrouped variables"}, "ab11": {"name": "ab11", "description": "", "definition": "a11*b11+a12*b21+a13*b31", "templateType": "anything", "group": "Ungrouped variables"}, "ab33": {"name": "ab33", "description": "", "definition": "a31*b13+a32*b23+a33*b33", "templateType": "anything", "group": "Ungrouped variables"}, "q1": {"name": "q1", "description": "", "definition": "b11*w1+b12*w2+b13*w3", "templateType": "anything", "group": "Ungrouped variables"}, "w": {"name": "w", "description": "", "definition": "random(3..5)", "templateType": "anything", "group": "Ungrouped variables"}, "ab23": {"name": "ab23", "description": "", "definition": "a21*b13+a22*b23+a23*b33", "templateType": "anything", "group": "Ungrouped variables"}, "v": {"name": "v", "description": "", "definition": "[[s1,-s1],[s2,-s2],[s3,-s3],[s4,-s4],[s5,-s5],[s6,-s6],[s7,-s7],[s8,-s8],[s9,-s9],[s10,-s10]]", "templateType": "anything", "group": "Ungrouped variables"}, "ba12": {"name": "ba12", "description": "", "definition": "b11*a12+b12*a22+b13*a32", "templateType": "anything", "group": "Ungrouped variables"}, "q3": {"name": "q3", "description": "", "definition": "b31*w1+b32*w2+b33*w3", "templateType": "anything", "group": "Ungrouped variables"}, "b23": {"name": "b23", "description": "", "definition": "random(1,2)", "templateType": "anything", "group": "Ungrouped variables"}, "s4": {"name": "s4", "description": "", "definition": "if(r=2,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables"}, "ba23": {"name": "ba23", "description": "", "definition": "b21*a13+b22*a23+b23*a33", "templateType": "anything", "group": "Ungrouped variables"}, "q": {"name": "q", "description": "", "definition": "m+random(0,z)", "templateType": "anything", "group": "Ungrouped variables"}, "s5": {"name": "s5", "description": "", "definition": "if(m=3,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables"}, "w3": {"name": "w3", "description": "", "definition": "random(-4..4)", "templateType": "anything", "group": "Ungrouped variables"}, "mae": {"name": "mae", "description": "", "definition": "matrix(repeat(repeat(random(-2..9),s),r))", "templateType": "anything", "group": "Ungrouped variables"}, "z": {"name": "z", "description": "", "definition": "random(-2,-1,1,2)", "templateType": "anything", "group": "Ungrouped variables"}, "a12": {"name": "a12", "description": "", "definition": "random(-1,1,2)", "templateType": "anything", "group": "Ungrouped variables"}, "mad": {"name": "mad", "description": "", "definition": "matrix(repeat(repeat(random(-2..9),q),p))", "templateType": "anything", "group": "Ungrouped variables"}, "a31": {"name": "a31", "description": "", "definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables"}, "ba13": {"name": "ba13", "description": "", "definition": "b11*a13+b12*a23+b13*a33", "templateType": "anything", "group": "Ungrouped variables"}, "c12": {"name": "c12", "description": "", "definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables"}, "ab13": {"name": "ab13", "description": "", "definition": "a11*b13+a12*b23+a13*b33", "templateType": "anything", "group": "Ungrouped variables"}, "p1": {"name": "p1", "description": "", "definition": "a11*v1+a12*v2+a13*v3", "templateType": "anything", "group": "Ungrouped variables"}, "ab31": {"name": "ab31", "description": "", "definition": "a31*b11+a32*b21+a33*b31", "templateType": "anything", "group": "Ungrouped variables"}, "p3": {"name": "p3", "description": "", "definition": "a31*v1+a32*v2+a33*v3", "templateType": "anything", "group": "Ungrouped variables"}, "x": {"name": "x", "description": "", "definition": "u+random(0,z)", "templateType": "anything", "group": "Ungrouped variables"}, "b12": {"name": "b12", "description": "", "definition": "random(0,1)", "templateType": "anything", "group": "Ungrouped variables"}, "b33": {"name": "b33", "description": "", "definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables"}, "b13": {"name": "b13", "description": "", "definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables"}, "s6": {"name": "s6", "description": "", "definition": "if(r=3,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables"}, "n": {"name": "n", "description": "", "definition": "random(3..6 except m)", "templateType": "anything", "group": "Ungrouped variables"}, "q2": {"name": "q2", "description": "", "definition": "b21*w1+b22*w2+b23*w3", "templateType": "anything", "group": "Ungrouped variables"}, "ba22": {"name": "ba22", "description": "", "definition": "b21*a12+b22*a22+b23*a32", "templateType": "anything", "group": "Ungrouped variables"}, "ba33": {"name": "ba33", "description": "", "definition": "b31*a13+b32*a23+b33*a33", "templateType": "anything", "group": "Ungrouped variables"}, "w1": {"name": "w1", "description": "", "definition": "random(4..6)", "templateType": "anything", "group": "Ungrouped variables"}, "s1": {"name": "s1", "description": "", "definition": "if(n=p,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables"}, "mag": {"name": "mag", "description": "", "definition": "matrix(repeat(repeat(random(-2..9),u),w))", "templateType": "anything", "group": "Ungrouped variables"}, "s10": {"name": "s10", "description": "", "definition": "if(u=3,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables"}, "m": {"name": "m", "description": "", "definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables"}, "mah": {"name": "mah", "description": "", "definition": "matrix(repeat(repeat(random(-2..9),x),y))", "templateType": "anything", "group": "Ungrouped variables"}, "a32": {"name": "a32", "description": "", "definition": "random(-4..4)", "templateType": "anything", "group": "Ungrouped variables"}, "u": {"name": "u", "description": "", "definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables"}, "a33": {"name": "a33", "description": "", "definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables"}, "c11": {"name": "c11", "description": "", "definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables"}, "v1": {"name": "v1", "description": "", "definition": "random(-3..3)", "templateType": "anything", "group": "Ungrouped variables"}, "p2": {"name": "p2", "description": "", "definition": "a21*v1+a22*v2+a23*v3", "templateType": "anything", "group": "Ungrouped variables"}, "a21": {"name": "a21", "description": "", "definition": "random(-1,0,1)", "templateType": "anything", "group": "Ungrouped variables"}, "b11": {"name": "b11", "description": "", "definition": "random(0,1)", "templateType": "anything", "group": "Ungrouped variables"}, "a22": {"name": "a22", "description": "", "definition": "random(-4,-3,-2,-1,1,2,3,5)", "templateType": "anything", "group": "Ungrouped variables"}, "mac": {"name": "mac", "description": "", "definition": "matrix(repeat(repeat(random(-2..9),n),m))", "templateType": "anything", "group": "Ungrouped variables"}, "a23": {"name": "a23", "description": "", "definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables"}, "b22": {"name": "b22", "description": "", "definition": "random(-4,-3,-2,-1,1,2,3,4)", "templateType": "anything", "group": "Ungrouped variables"}, "s": {"name": "s", "description": "", "definition": "random(4..6)", "templateType": "anything", "group": "Ungrouped variables"}, "ab22": {"name": "ab22", "description": "", "definition": "a21*b12+a22*b22+a23*b32", "templateType": "anything", "group": "Ungrouped variables"}, "b31": {"name": "b31", "description": "", "definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables"}, "b32": {"name": "b32", "description": "", "definition": "random(-3..3)", "templateType": "anything", "group": "Ungrouped variables"}, "s7": {"name": "s7", "description": "", "definition": "if(u=y,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables"}, "a13": {"name": "a13", "description": "", "definition": "random(1..2)", "templateType": "anything", "group": "Ungrouped variables"}, "b21": {"name": "b21", "description": "", "definition": "random(0..2)", "templateType": "anything", "group": "Ungrouped variables"}, "ab32": {"name": "ab32", "description": "", "definition": "a31*b12+a32*b22+a33*b32", "templateType": "anything", "group": "Ungrouped variables"}, "s9": {"name": "s9", "description": "", "definition": "if(w=3,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables"}, "s2": {"name": "s2", "description": "", "definition": "if(q=m,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables"}, "ba11": {"name": "ba11", "description": "", "definition": "b11*a11+b12*a21+b13*a31", "templateType": "anything", "group": "Ungrouped variables"}, "y": {"name": "y", "description": "", "definition": "u+random(0,z)", "templateType": "anything", "group": "Ungrouped variables"}, "s8": {"name": "s8", "description": "", "definition": "if(x=r,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables"}, "v2": {"name": "v2", "description": "", "definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables"}, "s3": {"name": "s3", "description": "", "definition": "if(s=5,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables"}, "v3": {"name": "v3", "description": "", "definition": "random(-5..5)", "templateType": "anything", "group": "Ungrouped variables"}, "a11": {"name": "a11", "description": "", "definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables"}, "w2": {"name": "w2", "description": "", "definition": "random(-4..4)", "templateType": "anything", "group": "Ungrouped variables"}, "p": {"name": "p", "description": "", "definition": "n+random(0,z)", "templateType": "anything", "group": "Ungrouped variables"}, "ab21": {"name": "ab21", "description": "", "definition": "a21*b11+a22*b21+a23*b31", "templateType": "anything", "group": "Ungrouped variables"}, "ba21": {"name": "ba21", "description": "", "definition": "b21*a11+b22*a21+b23*a31", "templateType": "anything", "group": "Ungrouped variables"}, "r": {"name": "r", "description": "", "definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables"}, "ba32": {"name": "ba32", "description": "", "definition": "b31*a12+b32*a22+b33*a32", "templateType": "anything", "group": "Ungrouped variables"}, "ab12": {"name": "ab12", "description": "", "definition": "a11*b12+a12*b22+a13*b32", "templateType": "anything", "group": "Ungrouped variables"}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Elementary Exercises in multiplying matrices.&nbsp;</p>"}, "type": "question", "contributors": [{"name": "Alex Van den Hof", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1273/"}]}]}], "contributors": [{"name": "Alex Van den Hof", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1273/"}]}