// Numbas version: finer_feedback_settings
{"name": "Solve a 3 x 3 matrix system", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "statement": "<p>Solve the following matrix equation \\[\\begin{pmatrix}2 &amp; \\var{b1} &amp; 3 \\\\5 &amp; 6 &amp; \\var{c1} \\\\\\var{a1} &amp; 2 &amp; 4\\end{pmatrix}\\begin{pmatrix}x \\\\ y \\\\ z\\end{pmatrix}=\\begin{pmatrix}\\var{r2} \\\\ \\var{r3} \\\\ \\var{r1}\\end{pmatrix}\\]</p>\n<p></p>", "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "<p>Solve a 3 x 3 matrix system.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "parts": [{"showFeedbackIcon": true, "showCorrectAnswer": true, "gaps": [{"showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "minValue": "((18-{b1}*{c1})*(3*{r1}-{r3})+({c1}-12)*(6*{r2}-{b1}*{r3}))/((3*{a1}-5)*(18-{b1}*{c1})-(12-5*{b1})*(12-{c1}))", "showPrecisionHint": true, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "precisionPartialCredit": 0, "strictPrecision": false, "precision": "3", "mustBeReducedPC": 0, "showFeedbackIcon": true, "scripts": {}, "precisionType": "dp", "mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "((18-{b1}*{c1})*(3*{r1}-{r3})+({c1}-12)*(6*{r2}-{b1}*{r3}))/((3*{a1}-5)*(18-{b1}*{c1})-(12-5*{b1})*(12-{c1}))", "type": "numberentry", "marks": 1, "notationStyles": ["plain", "en", "si-en"]}, {"showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "minValue": "((15-2*{c1})*(2*{r1}-{a1}*{r2})+(3*{a1}-8)*(5*{r2}-2*{r3}))/((4-{a1}*{b1})*(15-2*{c1})-(5*{b1}-12)*(8-3*{a1}))", "showPrecisionHint": true, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "precisionPartialCredit": 0, "strictPrecision": false, "precision": "3", "mustBeReducedPC": 0, "showFeedbackIcon": true, "scripts": {}, "precisionType": "dp", "mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "((15-2*{c1})*(2*{r1}-{a1}*{r2})+(3*{a1}-8)*(5*{r2}-2*{r3}))/((4-{a1}*{b1})*(15-2*{c1})-(5*{b1}-12)*(8-3*{a1}))", "type": "numberentry", "marks": 1, "notationStyles": ["plain", "en", "si-en"]}, {"showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "minValue": "((12-5*{b1})*(2*{r1}-{a1}*{r2})+(4-{b1}*{a1})*(5*{r2}-2*{r3}))/((4-{a1}*{b1})*(15-2*{c1})-(5*{b1}-12)*(8-3*{a1}))", "showPrecisionHint": true, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "variableReplacements": [], "precisionPartialCredit": 0, "strictPrecision": false, "precision": "3", "mustBeReducedPC": 0, "showFeedbackIcon": true, "scripts": {}, "precisionType": "dp", "mustBeReduced": false, "correctAnswerFraction": false, "maxValue": "((12-5*{b1})*(2*{r1}-{a1}*{r2})+(4-{b1}*{a1})*(5*{r2}-2*{r3}))/((4-{a1}*{b1})*(15-2*{c1})-(5*{b1}-12)*(8-3*{a1}))", "type": "numberentry", "marks": 1, "notationStyles": ["plain", "en", "si-en"]}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "type": "gapfill", "variableReplacements": [], "prompt": "<p>Input the values of \\(x\\), \\(y\\) and \\(z\\) that satisfy the equations.</p>\n<p style=\"padding-left: 30px;\">\\(x = \\)&nbsp;[[0]]</p>\n<p style=\"padding-left: 30px;\">\\(y = \\)&nbsp;[[1]]</p>\n<p style=\"padding-left: 30px;\">\\(z = \\)&nbsp;[[2]]</p>", "marks": 0}], "functions": {}, "preamble": {"js": "", "css": ""}, "variables": {"c1": {"definition": "random(3..12#1)", "description": "", "name": "c1", "templateType": "randrange", "group": "Ungrouped variables"}, "r1": {"definition": "random(20..42#1)", "description": "", "name": "r1", "templateType": "randrange", "group": "Ungrouped variables"}, "r3": {"definition": "random(30..60#1)", "description": "", "name": "r3", "templateType": "randrange", "group": "Ungrouped variables"}, "r2": {"definition": "random(18..50#1)", "description": "", "name": "r2", "templateType": "randrange", "group": "Ungrouped variables"}, "a1": {"definition": "random(2..8#1)", "description": "", "name": "a1", "templateType": "randrange", "group": "Ungrouped variables"}, "b1": {"definition": "random(2..10#1)", "description": "", "name": "b1", "templateType": "randrange", "group": "Ungrouped variables"}}, "rulesets": {}, "variable_groups": [], "ungrouped_variables": ["a1", "b1", "c1", "r1", "r2", "r3"], "name": "Solve a 3 x 3 matrix system", "advice": "<p>Use augmented matrices to solve this.</p>", "tags": [], "type": "question", "contributors": [{"name": "Timothy Gould", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1466/"}]}]}], "contributors": [{"name": "Timothy Gould", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1466/"}]}