// Numbas version: finer_feedback_settings {"name": "Blathnaid's copy of Matrix multiplication", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "

Elementary Exercises in multiplying matrices. 

", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "name": "Blathnaid's copy of Matrix multiplication", "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"sortAnswers": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "gaps": [{"maxValue": "{p1}", "minValue": "{p1}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{p2}", "minValue": "{p2}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{p3}", "minValue": "{p3}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{q1}", "minValue": "{q1}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{q2}", "minValue": "{q2}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{q3}", "minValue": "{q3}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ba11}", "minValue": "{ba11}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ba12}", "minValue": "{ba12}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ba13}", "minValue": "{ba13}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ba21}", "minValue": "{ba21}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ba22}", "minValue": "{ba22}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ba23}", "minValue": "{ba23}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ba31}", "minValue": "{ba31}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ba32}", "minValue": "{ba32}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ba33}", "minValue": "{ba33}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ab11}", "minValue": "{ab11}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ab12}", "minValue": "{ab12}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ab13}", "minValue": "{ab13}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ab21}", "minValue": "{ab21}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ab22}", "minValue": "{ab22}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ab23}", "minValue": "{ab23}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ab31}", "minValue": "{ab31}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ab32}", "minValue": "{ab32}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}, {"maxValue": "{ab33}", "minValue": "{ab33}", "correctAnswerStyle": "plain", "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "mustBeReduced": false, "customMarkingAlgorithm": "", "correctAnswerFraction": false, "unitTests": [], "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "mustBeReducedPC": 0, "type": "numberentry", "allowFractions": false, "showCorrectAnswer": true, "marks": 0.5}], "variableReplacements": [], "customMarkingAlgorithm": "", "prompt": "\n \n \n

Let

\n \n \n \n

\\[A = \\left(\\begin{array}{rrr} \\var{a11} & \\var{a12} & \\var{a13}\\\\ \\var{a21} & \\var{a22} & \\var{a23}\\\\ \\var{a31} & \\var{a32} & \\var{a33}\\\\\n \n \\end{array}\\right),\\;\\;\\;\\;\n \n B= \\left(\\begin{array}{rrr} \\var{b11} & \\var{b12} & \\var{b13}\\\\ \\var{b21} & \\var{b22} & \\var{b23}\\\\ \\var{b31} & \\var{b32} & \\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)\\]

\n \n \n \n

Find the following products:

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
\\[ Av=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\] [[0]] \\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]
[[1]]
[[2]]
\\[ Bw=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\] [[3]] \\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]
[[4]]
[[5]]
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
\\[BA=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\] [[6]] [[7]] [[8]] \\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]
[[9]] [[10]] [[11]]
[[12]] [[13]] [[14]]
\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n
\\[AB=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\] [[15]] [[16]] [[17]] \\[\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\\]
[[18]] [[19]] [[20]]
[[21]] [[22]] [[23]]
\n \n \n \n ", "unitTests": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "type": "gapfill", "showCorrectAnswer": true, "marks": 0}], "variable_groups": [], "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"], "extensions": ["stats"], "tags": [], "statement": "

Answer the following questions on matrices.

\n

 

", "advice": "", "functions": {}, "variables": {"ab31": {"description": "", "group": "Ungrouped variables", "name": "ab31", "definition": "a31*b11+a32*b21+a33*b31", "templateType": "anything"}, "w": {"description": "", "group": "Ungrouped variables", "name": "w", "definition": "random(3..5)", "templateType": "anything"}, "mag": {"description": "", "group": "Ungrouped variables", "name": "mag", "definition": "matrix(repeat(repeat(random(-2..9),u),w))", "templateType": "anything"}, "s5": {"description": "", "group": "Ungrouped variables", "name": "s5", "definition": "if(m=3,0.5,-0.5)", "templateType": "anything"}, "c11": {"description": "", "group": "Ungrouped variables", "name": "c11", "definition": "random(-2..2)", "templateType": "anything"}, "ba21": {"description": "", "group": "Ungrouped variables", "name": "ba21", "definition": "b21*a11+b22*a21+b23*a31", "templateType": "anything"}, "y": {"description": "", "group": "Ungrouped variables", "name": "y", "definition": "u+random(0,z)", "templateType": "anything"}, "p2": {"description": "", "group": "Ungrouped variables", "name": "p2", "definition": "a21*v1+a22*v2+a23*v3", "templateType": "anything"}, "s8": {"description": "", "group": "Ungrouped variables", "name": "s8", "definition": "if(x=r,0.5,-0.5)", "templateType": "anything"}, "ab32": {"description": "", "group": "Ungrouped variables", "name": "ab32", "definition": "a31*b12+a32*b22+a33*b32", "templateType": "anything"}, "s3": {"description": "", "group": "Ungrouped variables", "name": "s3", "definition": "if(s=5,0.5,-0.5)", "templateType": "anything"}, "ba11": {"description": "", "group": "Ungrouped variables", "name": "ba11", "definition": "b11*a11+b12*a21+b13*a31", "templateType": "anything"}, "q1": {"description": "", "group": "Ungrouped variables", "name": "q1", "definition": "b11*w1+b12*w2+b13*w3", "templateType": "anything"}, "ba12": {"description": "", "group": "Ungrouped variables", "name": "ba12", "definition": "b11*a12+b12*a22+b13*a32", "templateType": "anything"}, "r": {"description": "", "group": "Ungrouped variables", "name": "r", "definition": "random(1..3)", "templateType": "anything"}, "m": {"description": "", "group": "Ungrouped variables", "name": "m", "definition": "random(3..4)", "templateType": "anything"}, "a13": {"description": "", "group": "Ungrouped variables", "name": "a13", "definition": "random(1..2)", "templateType": "anything"}, "b12": {"description": "", "group": "Ungrouped variables", "name": "b12", "definition": "random(0,1)", "templateType": "anything"}, "c13": {"description": "", "group": "Ungrouped variables", "name": "c13", "definition": "random(1..2)", "templateType": "anything"}, "a11": {"description": "", "group": "Ungrouped variables", "name": "a11", "definition": "random(1..4)", "templateType": "anything"}, "ba23": {"description": "", "group": "Ungrouped variables", "name": "ba23", "definition": "b21*a13+b22*a23+b23*a33", "templateType": "anything"}, "ba22": {"description": "", "group": "Ungrouped variables", "name": "ba22", "definition": "b21*a12+b22*a22+b23*a32", "templateType": "anything"}, "a33": {"description": "", "group": "Ungrouped variables", "name": "a33", "definition": "random(1..4)", "templateType": "anything"}, "u": {"description": "", "group": "Ungrouped variables", "name": "u", "definition": "random(3..4)", "templateType": "anything"}, "w3": {"description": "", "group": "Ungrouped variables", "name": "w3", "definition": "random(-4..4)", "templateType": "anything"}, "q": {"description": "", "group": "Ungrouped variables", "name": "q", "definition": "m+random(0,z)", "templateType": "anything"}, "a22": {"description": "", "group": "Ungrouped variables", "name": "a22", "definition": "random(-4,-3,-2,-1,1,2,3,5)", "templateType": "anything"}, "mah": {"description": "", "group": "Ungrouped variables", "name": "mah", "definition": "matrix(repeat(repeat(random(-2..9),x),y))", "templateType": "anything"}, "mad": {"description": "", "group": "Ungrouped variables", "name": "mad", "definition": "matrix(repeat(repeat(random(-2..9),q),p))", "templateType": "anything"}, "q3": {"description": "", "group": "Ungrouped variables", "name": "q3", "definition": "b31*w1+b32*w2+b33*w3", "templateType": "anything"}, "p1": {"description": "", "group": "Ungrouped variables", "name": "p1", "definition": "a11*v1+a12*v2+a13*v3", "templateType": "anything"}, "a32": {"description": "", "group": "Ungrouped variables", "name": "a32", "definition": "random(-4..4)", "templateType": "anything"}, "x": {"description": "", "group": "Ungrouped variables", "name": "x", "definition": "u+random(0,z)", "templateType": "anything"}, "ba32": {"description": "", "group": "Ungrouped variables", "name": "ba32", "definition": "b31*a12+b32*a22+b33*a32", "templateType": "anything"}, "v2": {"description": "", "group": "Ungrouped variables", "name": "v2", "definition": "random(1..4)", "templateType": "anything"}, "b23": {"description": "", "group": "Ungrouped variables", "name": "b23", "definition": "random(1,2)", "templateType": "anything"}, "s": {"description": "", "group": "Ungrouped variables", "name": "s", "definition": "random(4..6)", "templateType": "anything"}, "p": {"description": "", "group": "Ungrouped variables", "name": "p", "definition": "n+random(0,z)", "templateType": "anything"}, "v1": {"description": "", "group": "Ungrouped variables", "name": "v1", "definition": "random(-3..3)", "templateType": "anything"}, "ab22": {"description": "", "group": "Ungrouped variables", "name": "ab22", "definition": "a21*b12+a22*b22+a23*b32", "templateType": "anything"}, "mae": {"description": "", "group": "Ungrouped variables", "name": "mae", "definition": "matrix(repeat(repeat(random(-2..9),s),r))", "templateType": "anything"}, "z": {"description": "", "group": "Ungrouped variables", "name": "z", "definition": "random(-2,-1,1,2)", "templateType": "anything"}, "mac": {"description": "", "group": "Ungrouped variables", "name": "mac", "definition": "matrix(repeat(repeat(random(-2..9),n),m))", "templateType": "anything"}, "v": {"description": "", "group": "Ungrouped variables", "name": "v", "definition": "[[s1,-s1],[s2,-s2],[s3,-s3],[s4,-s4],[s5,-s5],[s6,-s6],[s7,-s7],[s8,-s8],[s9,-s9],[s10,-s10]]", "templateType": "anything"}, "ab21": {"description": "", "group": "Ungrouped variables", "name": "ab21", "definition": "a21*b11+a22*b21+a23*b31", "templateType": "anything"}, "q2": {"description": "", "group": "Ungrouped variables", "name": "q2", "definition": "b21*w1+b22*w2+b23*w3", "templateType": "anything"}, "a23": {"description": "", "group": "Ungrouped variables", "name": "a23", "definition": "random(-2..2)", "templateType": "anything"}, "w2": {"description": "", "group": "Ungrouped variables", "name": "w2", "definition": "random(-4..4)", "templateType": "anything"}, "s1": {"description": "", "group": "Ungrouped variables", "name": "s1", "definition": "if(n=p,0.5,-0.5)", "templateType": "anything"}, "a31": {"description": "", "group": "Ungrouped variables", "name": "a31", "definition": "random(1..3)", "templateType": "anything"}, "v3": {"description": "", "group": "Ungrouped variables", "name": "v3", "definition": "random(-5..5)", "templateType": "anything"}, "n": {"description": "", "group": "Ungrouped variables", "name": "n", "definition": "random(3..6 except m)", "templateType": "anything"}, "c12": {"description": "", "group": "Ungrouped variables", "name": "c12", "definition": "random(1..3)", "templateType": "anything"}, "s10": {"description": "", "group": "Ungrouped variables", "name": "s10", "definition": "if(u=3,0.5,-0.5)", "templateType": "anything"}, "b33": {"description": "", "group": "Ungrouped variables", "name": "b33", "definition": "random(-2..2)", "templateType": "anything"}, "s9": {"description": "", "group": "Ungrouped variables", "name": "s9", "definition": "if(w=3,0.5,-0.5)", "templateType": "anything"}, "s4": {"description": "", "group": "Ungrouped variables", "name": "s4", "definition": "if(r=2,0.5,-0.5)", "templateType": "anything"}, "ab23": {"description": "", "group": "Ungrouped variables", "name": "ab23", "definition": "a21*b13+a22*b23+a23*b33", "templateType": "anything"}, "a21": {"description": "", "group": "Ungrouped variables", "name": "a21", "definition": "random(-1,0,1)", "templateType": "anything"}, "b22": {"description": "", "group": "Ungrouped variables", "name": "b22", "definition": "random(-4,-3,-2,-1,1,2,3,4)", "templateType": "anything"}, "b31": {"description": "", "group": "Ungrouped variables", "name": "b31", "definition": "random(1..3)", "templateType": "anything"}, "ab12": {"description": "", "group": "Ungrouped variables", "name": "ab12", "definition": "a11*b12+a12*b22+a13*b32", "templateType": "anything"}, "b32": {"description": "", "group": "Ungrouped variables", "name": "b32", "definition": "random(-3..3)", "templateType": "anything"}, "w1": {"description": "", "group": "Ungrouped variables", "name": "w1", "definition": "random(4..6)", "templateType": "anything"}, "ab13": {"description": "", "group": "Ungrouped variables", "name": "ab13", "definition": "a11*b13+a12*b23+a13*b33", "templateType": "anything"}, "ba13": {"description": "", "group": "Ungrouped variables", "name": "ba13", "definition": "b11*a13+b12*a23+b13*a33", "templateType": "anything"}, "p3": {"description": "", "group": "Ungrouped variables", "name": "p3", "definition": "a31*v1+a32*v2+a33*v3", "templateType": "anything"}, "s2": {"description": "", "group": "Ungrouped variables", "name": "s2", "definition": "if(q=m,0.5,-0.5)", "templateType": "anything"}, "ab33": {"description": "", "group": "Ungrouped variables", "name": "ab33", "definition": "a31*b13+a32*b23+a33*b33", "templateType": "anything"}, "a12": {"description": "", "group": "Ungrouped variables", "name": "a12", "definition": "random(-1,1,2)", "templateType": "anything"}, "b13": {"description": "", "group": "Ungrouped variables", "name": "b13", "definition": "random(-2..2)", "templateType": "anything"}, "b21": {"description": "", "group": "Ungrouped variables", "name": "b21", "definition": "random(0..2)", "templateType": "anything"}, "s7": {"description": "", "group": "Ungrouped variables", "name": "s7", "definition": "if(u=y,0.5,-0.5)", "templateType": "anything"}, "b11": {"description": "", "group": "Ungrouped variables", "name": "b11", "definition": "random(0,1)", "templateType": "anything"}, "ab11": {"description": "", "group": "Ungrouped variables", "name": "ab11", "definition": "a11*b11+a12*b21+a13*b31", "templateType": "anything"}, "ba33": {"description": "", "group": "Ungrouped variables", "name": "ba33", "definition": "b31*a13+b32*a23+b33*a33", "templateType": "anything"}, "s6": {"description": "", "group": "Ungrouped variables", "name": "s6", "definition": "if(r=3,0.5,-0.5)", "templateType": "anything"}, "ba31": {"description": "", "group": "Ungrouped variables", "name": "ba31", "definition": "b31*a11+b32*a21+b33*a31", "templateType": "anything"}}, "preamble": {"js": "", "css": ""}, "type": "question", "contributors": [{"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Blathnaid Sheridan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/447/"}, {"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}