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{"name": "EG3101 EG5116 EG4103 Matrices: determinant and inverse of a 2x2 matrix", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"inv": {"definition": "matrix([[matrixA[1][1],-matrixA[0][1]],[-matrixA[1][0],matrixA[0][0]]])/det(matrixA)", "type": "matrix", "language": "jme", "parameters": [["matrixA", "matrix"]]}}, "ungrouped_variables": ["matrixA", "a11", "a12", "a21", "a22"], "name": "EG3101 EG5116 EG4103 Matrices: determinant and inverse of a 2x2 matrix", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>If \\[&nbsp; A=\\left( \\begin{array}{ccc}<br/>a &amp; b&nbsp; \\\\<br/>c&nbsp;&amp;&nbsp;d&nbsp; \\end{array} \\right),\\]</p>\n<p>Then, the determinant is given by \\[{ad-bc}\\]</p>\n<p>and the inverse of A = \\[&nbsp;\\frac{1}{ad-bc} \\left( \\begin{array}{ccc}<br/>d &amp; -b&nbsp; \\\\<br/>-c&nbsp;&amp;&nbsp;a&nbsp; \\end{array} \\right),\\]</p>\n<p><span class=\"nb\">&nbsp;</span></p>\n<p><span class=\"nb\"><span class=\"k\"><span class=\"s\">&nbsp;</span></span></span></p>\n<p></p>", "rulesets": {}, "parts": [{"prompt": "<p>What is the determinant of A=$\\var{matrixA}$?</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "det(matrixA)", "minValue": "det(matrixA)", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>What is the&nbsp;inverse of A=$\\var{matrixA}$?</p>\n<p>[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"numRows": "2", "numColumns": "2", "allowResize": true, "allowFractions": false, "variableReplacements": [], "markPerCell": false, "variableReplacementStrategy": "originalfirst", "tolerance": "0.005", "correctAnswerFractions": false, "showCorrectAnswer": true, "correctAnswer": "inv(matrixA)", "scripts": {}, "marks": 1, "type": "matrix"}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a21": {"definition": "random(0..100)/10", "templateType": "anything", "group": "Ungrouped variables", "name": "a21", "description": ""}, "a22": {"definition": "random(0..100 except(a21*a12/a11))/10", "templateType": "anything", "group": "Ungrouped variables", "name": "a22", "description": ""}, "matrixA": {"definition": "matrix([a11,a12],[a21,a22])", "templateType": "anything", "group": "Ungrouped variables", "name": "matrixA", "description": ""}, "a11": {"definition": "random(0..100)/10", "templateType": "anything", "group": "Ungrouped variables", "name": "a11", "description": ""}, "a12": {"definition": "random(0..100)/10", "templateType": "anything", "group": "Ungrouped variables", "name": "a12", "description": ""}}, "metadata": {"description": "<p>Determinant and inverse of a 2x2 matrix.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "contributors": [{"name": "bryan pearce", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/347/"}]}]}], "contributors": [{"name": "bryan pearce", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/347/"}]}