// Numbas version: finer_feedback_settings
{"name": "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": "Simon's copy of Matrices: Manipulation, ", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "", "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"}, {"prompt": "<p>Consider the following matrices together with the matrices from the first part of the question.</p>\n        <p>\\[\\begin{eqnarray}&amp;C=&amp; \\var{mac},\\;\\;\\;\\; &amp;D=&amp; \\var{mad},\\;\\;\\; \\;&amp;E= &amp;\\var{mae}\\\\&amp;F=&amp; \\left(\\begin{array}{rr} \\var{w1} &amp; \\var{a12}\\\\ \\var{w2} &amp; \\var{b23} \\\\ \\var{w3} &amp; \\var{w2} \\\\\\var{v1} &amp; \\var{b12}\\\\ 0 &amp; \\var{-w2} \\end{array}\\right),\\;\\;\\;\\;&amp;G=&amp;\\var{mag},\\;\\;\\;\\;&amp;H=&amp;\\var{mah} \\end{eqnarray}\\]</p>\n        <p>Which of the following products of matrices can be calculated?</p>\n        <p>[[0]]</p>\n        <p><strong>Please note that for every correct answer you get 0.5 marks and for every incorrect answer 0.5 is taken away. The minimum mark you can get is 0.</strong></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"maxAnswers": 0, "shuffleChoices": true, "matrix": "v", "shuffleAnswers": false, "minAnswers": 0, "variableReplacements": [], "answers": ["<strong>Can be calculated</strong>", "<strong>Cannot be calculated</strong>"], "warningType": "none", "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "showCorrectAnswer": true, "scripts": {}, "marks": 0, "choices": ["<p>$CD$</p>", "<p>$DC$</p>", "<p>$EF$</p>", "<p>$FE$</p>", "<p>$BC$</p>", "<p>$AE$</p>", "<p>$GH$</p>", "<p>$HE$</p>", "<p>$AG$</p>", "<p>$GB$</p>"], "type": "m_n_x", "displayType": "radiogroup", "minMarks": 0, "layout": {"expression": "", "type": "all"}}], "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": ""}, "a12": {"definition": "random(-1,1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a12", "description": ""}, "s7": {"definition": "if(u=y,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s7", "description": ""}, "s6": {"definition": "if(r=3,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s6", "description": ""}, "s5": {"definition": "if(m=3,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s5", "description": ""}, "s4": {"definition": "if(r=2,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s4", "description": ""}, "b12": {"definition": "random(0,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b12", "description": ""}, "b13": {"definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b13", "description": ""}, "b11": {"definition": "random(0,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b11", "description": ""}, "c13": {"definition": "random(1..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "c13", "description": ""}, "c12": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "c12", "description": ""}, "c11": {"definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "c11", "description": ""}, "a33": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a33", "description": ""}, "a32": {"definition": "random(-4..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a32", "description": ""}, "a31": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "a31", "description": ""}, "ba32": {"definition": "b31*a12+b32*a22+b33*a32", "templateType": "anything", "group": "Ungrouped variables", "name": "ba32", "description": ""}, "ba33": {"definition": "b31*a13+b32*a23+b33*a33", "templateType": "anything", "group": "Ungrouped variables", "name": "ba33", "description": ""}, "a13": {"definition": "random(1..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a13", "description": ""}, "ba31": {"definition": "b31*a11+b32*a21+b33*a31", "templateType": "anything", "group": "Ungrouped variables", "name": "ba31", "description": ""}, "s10": {"definition": "if(u=3,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s10", "description": ""}, "s9": {"definition": "if(w=3,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s9", "description": ""}, "b32": {"definition": "random(-3..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "b32", "description": ""}, "b31": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "b31", "description": ""}, "v1": {"definition": "random(-3..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "v1", "description": ""}, "v2": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "v2", "description": ""}, "v3": {"definition": "random(-5..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "v3", "description": ""}, "mae": {"definition": "matrix(repeat(repeat(random(-2..9),s),r))", "templateType": "anything", "group": "Ungrouped variables", "name": "mae", "description": ""}, "mad": {"definition": "matrix(repeat(repeat(random(-2..9),q),p))", "templateType": "anything", "group": "Ungrouped variables", "name": "mad", "description": ""}, "mag": {"definition": "matrix(repeat(repeat(random(-2..9),u),w))", "templateType": "anything", "group": "Ungrouped variables", "name": "mag", "description": ""}, "mah": {"definition": "matrix(repeat(repeat(random(-2..9),x),y))", "templateType": "anything", "group": "Ungrouped variables", "name": "mah", "description": ""}, "ba12": {"definition": "b11*a12+b12*a22+b13*a32", "templateType": "anything", "group": "Ungrouped variables", "name": "ba12", "description": ""}, "ba13": {"definition": "b11*a13+b12*a23+b13*a33", "templateType": "anything", "group": "Ungrouped variables", "name": "ba13", "description": ""}, "b33": {"definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b33", "description": ""}, "p2": {"definition": "a21*v1+a22*v2+a23*v3", "templateType": "anything", "group": "Ungrouped variables", "name": "p2", "description": ""}, "p3": {"definition": "a31*v1+a32*v2+a33*v3", "templateType": "anything", "group": "Ungrouped variables", "name": "p3", "description": ""}, "ba23": {"definition": "b21*a13+b22*a23+b23*a33", "templateType": "anything", "group": "Ungrouped variables", "name": "ba23", "description": ""}, "ab11": {"definition": "a11*b11+a12*b21+a13*b31", "templateType": "anything", "group": "Ungrouped variables", "name": "ab11", "description": ""}, "s8": {"definition": "if(x=r,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s8", "description": ""}, "ab31": {"definition": "a31*b11+a32*b21+a33*b31", "templateType": "anything", "group": "Ungrouped variables", "name": "ab31", "description": ""}, "ab32": {"definition": "a31*b12+a32*b22+a33*b32", "templateType": "anything", "group": "Ungrouped variables", "name": "ab32", "description": ""}, "ab33": {"definition": "a31*b13+a32*b23+a33*b33", "templateType": "anything", "group": "Ungrouped variables", "name": "ab33", "description": ""}, "ab12": {"definition": "a11*b12+a12*b22+a13*b32", "templateType": "anything", "group": "Ungrouped variables", "name": "ab12", "description": ""}, "m": {"definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "mac": {"definition": "matrix(repeat(repeat(random(-2..9),n),m))", "templateType": "anything", "group": "Ungrouped variables", "name": "mac", "description": ""}, "n": {"definition": "random(3..6 except m)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "m+random(0,z)", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "n+random(0,z)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "random(4..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": 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