// Numbas version: exam_results_page_options
{"name": "Invert a 3 x 3 matrix", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": [], "metadata": {"description": "<p>Invert a 3 x 3 matrix.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["c1", "g1", "h1", "i1", "f1", "MINV", "M", "MR1", "MR2"], "advice": "<p>The first step of augmented matrix reduction gives</p>\n<p>\\[\\var{MR1}\\]</p>\n<p>Note - the | is implied after the third entry on each row.</p>\n<p>Since there are two leading 0s in the second row, we then do a simple swap of row 2 and 3.</p>\n<p>\\[\\var{MR2}\\]</p>", "variables": {"h1": {"name": "h1", "description": "", "definition": "2*g1", "templateType": "anything", "group": "Ungrouped variables"}, "MINV": {"name": "MINV", "description": "", "definition": "matrix([(2*f1-c1)*g1-1,c1-2*f1,2],[(2*c1-f1)*g1+2,f1-2*c1,-1],[-3*g1,3,0])/3", "templateType": "anything", "group": "Ungrouped variables"}, "c1": {"name": "c1", "description": "", "definition": "random(3..12#1)", "templateType": "randrange", "group": "Ungrouped variables"}, "M": {"name": "M", "description": "", "definition": "matrix([1,2,c1],[g1,2*g1,c1*g1+1],[2,1,f1])", "templateType": "anything", "group": "Ungrouped variables"}, "i1": {"name": "i1", "description": "", "definition": "c1*g1+1", "templateType": "anything", "group": "Ungrouped variables"}, "f1": {"name": "f1", "description": "", "definition": "random(-5..5#1)", "templateType": "randrange", "group": "Ungrouped variables"}, "g1": {"name": "g1", "description": "", "definition": "random(-5..5#1)", "templateType": "randrange", "group": "Ungrouped variables"}, "MR2": {"name": "MR2", "description": "<p>Second step of matrix inverse</p>", "definition": "matrix([1,2,c1,1,0,0],[0,-3,f1-2*c1,-2,0,1],[0,0,1,-g1,1,0])", "templateType": "anything", "group": "Ungrouped variables"}, "MR1": {"name": "MR1", "description": "<p>First step of matrix reduction for inverse</p>", "definition": "matrix([1,2,c1,1,0,0],[0,0,1,-g1,1,0],[0,-3,f1-2*c1,-2,0,1])", "templateType": "anything", "group": "Ungrouped variables"}}, "parts": [{"gaps": [{"variableReplacementStrategy": "originalfirst", "type": "matrix", "numRows": "3", "allowFractions": true, "showCorrectAnswer": true, "showFeedbackIcon": true, "allowResize": false, "markPerCell": false, "correctAnswerFractions": true, "scripts": {}, "correctAnswer": "MINV", "variableReplacements": [], "marks": "3", "tolerance": "0.01", "numColumns": "3"}], "variableReplacementStrategy": "originalfirst", "scripts": {}, "prompt": "<p style=\"padding-left: 30px;\">Input the inverse matrix<br/><br/>[[0]]</p>", "showFeedbackIcon": true, "showCorrectAnswer": true, "variableReplacements": [], "type": "gapfill", "marks": 0}], "variable_groups": [], "name": "Invert a 3 x 3 matrix", "rulesets": {}, "statement": "<p>Invert the following matrix</p>\n<p>\\[\\var{M}\\]</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/"}]}