// Numbas version: exam_results_page_options
{"name": "Alex's copy of Simon's copy of Matrices: Manipulation, ", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "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"], "name": "Alex's copy of Simon's copy of Matrices: Manipulation, ", "tags": [], "preamble": {"css": "", "js": ""}, "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>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "parts": [{"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>\n<tbody>\n<tr>\n<td rowspan=\"3\">\\[BA=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n<td>[[6]]</td>\n<td>[[7]]</td>\n<td>[[8]]</td>\n<td rowspan=\"3\">\\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]</td>\n</tr>\n<tr>\n<td>[[9]]</td>\n<td>[[10]]</td>\n<td>[[11]]</td>\n</tr>\n<tr>\n<td>[[12]]</td>\n<td>[[13]]</td>\n<td>[[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>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{p1}", "minValue": "{p1}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{p2}", "minValue": "{p2}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{p3}", "minValue": "{p3}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{q1}", "minValue": "{q1}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{q2}", "minValue": "{q2}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{q3}", "minValue": "{q3}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ba11}", "minValue": "{ba11}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ba12}", "minValue": "{ba12}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ba13}", "minValue": "{ba13}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ba21}", "minValue": "{ba21}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ba22}", "minValue": "{ba22}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ba23}", "minValue": "{ba23}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ba31}", "minValue": "{ba31}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ba32}", "minValue": "{ba32}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ba33}", "minValue": "{ba33}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ab11}", "minValue": "{ab11}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ab12}", "minValue": "{ab12}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ab13}", "minValue": "{ab13}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ab21}", "minValue": "{ab21}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ab22}", "minValue": "{ab22}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ab23}", "minValue": "{ab23}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ab31}", "minValue": "{ab31}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ab32}", "minValue": "{ab32}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{ab33}", "minValue": "{ab33}", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 0.5, "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": ["stats"], "statement": "<p>Answer the following questions on matrices.</p>\n    <p>&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ba21": {"definition": "b21*a11+b22*a21+b23*a31", "templateType": "anything", "group": "Ungrouped variables", "name": "ba21", "description": ""}, "a21": {"definition": "random(-1,0,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a21", "description": ""}, "a22": {"definition": "random(-4,-3,-2,-1,1,2,3,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a22", "description": ""}, "a23": {"definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a23", "description": ""}, "b23": {"definition": "random(1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b23", "description": ""}, "b22": {"definition": "random(-4,-3,-2,-1,1,2,3,4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b22", "description": ""}, "b21": {"definition": "random(0..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b21", "description": ""}, "ba22": {"definition": "b21*a12+b22*a22+b23*a32", "templateType": "anything", "group": "Ungrouped variables", "name": "ba22", "description": ""}, "w3": {"definition": "random(-4..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "w3", "description": ""}, "w2": {"definition": "random(-4..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "w2", "description": ""}, "w1": {"definition": "random(4..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "w1", "description": ""}, "ba11": {"definition": "b11*a11+b12*a21+b13*a31", "templateType": "anything", "group": "Ungrouped variables", "name": "ba11", "description": ""}, "a11": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a11", "description": ""}, "p1": {"definition": "a11*v1+a12*v2+a13*v3", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}, "q1": {"definition": "b11*w1+b12*w2+b13*w3", "templateType": "anything", "group": "Ungrouped variables", "name": "q1", "description": ""}, "q3": {"definition": "b31*w1+b32*w2+b33*w3", "templateType": "anything", "group": "Ungrouped variables", "name": "q3", "description": ""}, "q2": {"definition": "b21*w1+b22*w2+b23*w3", "templateType": "anything", "group": "Ungrouped variables", "name": "q2", "description": ""}, "ab23": {"definition": "a21*b13+a22*b23+a23*b33", "templateType": "anything", "group": "Ungrouped variables", "name": "ab23", "description": ""}, "ab22": {"definition": "a21*b12+a22*b22+a23*b32", "templateType": "anything", "group": "Ungrouped variables", "name": "ab22", "description": ""}, "ab21": {"definition": "a21*b11+a22*b21+a23*b31", "templateType": "anything", "group": "Ungrouped variables", "name": "ab21", "description": ""}, "s3": {"definition": "if(s=5,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s3", "description": ""}, "s2": {"definition": "if(q=m,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s2", "description": ""}, "s1": {"definition": "if(n=p,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": 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