// Numbas version: finer_feedback_settings
{"name": "Determinant of a 2x2 Matrix", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Determinant of a 2x2 Matrix", "tags": [], "metadata": {"description": "<p>Exercises on calculating the determinant of 2x2 and 3x3 matrices.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<h1>$2 \\times 2$ Matrix Determinants</h1>\n<p>Calculate the determinants of the following matrices.</p>", "advice": "<p>To find the determinant of a $2\\times2$ matrix, we use the following formula</p>\n<p>$$<br/>\\begin{vmatrix}<br/>a &amp; b \\\\<br/>c &amp; d \\\\<br/>\\end{vmatrix} = ad-bc<br/>$$</p>\n<p>Hence, we have:</p>\n<p><strong>a)</strong></p>\n<p>$$<br/>\\det \\boldsymbol{A} = \\var{maA[0][0]} \\times \\var{maA[1][1]} - \\var{maA[0][1]} \\times \\var{maa[1][0]} = \\var{det(maA)}<br/>$$</p>\n<p><strong>b)</strong></p>\n<p>$$<br/>\\det \\boldsymbol{B} = \\var{maB[0][0]} \\times \\var{maB[1][1]} - \\var{maB[0][1]} \\times \\var{maB[1][0]} = \\var{det(maB)}<br/>$$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"maA": {"name": "maA", "group": "Ungrouped variables", "definition": "matrixrandom(2,2)", "description": "", "templateType": "anything", "can_override": false}, "maB": {"name": "maB", "group": "Ungrouped variables", "definition": "matrixrandom(2,2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["maA", "maB"], "variable_groups": [], "functions": {"matrixrandom": {"parameters": [["rows", "integer"], ["columns", "number"]], "type": "matrix", "language": "jme", "definition": "matrix(repeat(repeat(random(0..9)*(random(1,1,1,-1)),columns),rows))"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the determinant of the matrix:</p>\n<p>$$<br/>\\boldsymbol{A} = \\simplify{{maA}}<br/>$$</p>\n<p style=\"text-align: left;\">$\\det \\boldsymbol{A} = $ [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "det(maA)", "maxValue": "det(maA)", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the determinant of the matrix:</p>\n<p>$$<br/>\\boldsymbol{B} = \\simplify{{maB}}<br/>$$</p>\n<p style=\"text-align: left;\">$\\det \\boldsymbol{B} = $ [[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "det(maB)", "maxValue": "det(maB)", "correctAnswerFraction": false, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Mark Patterson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5064/"}, {"name": "Tamsin Smith", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14108/"}, {"name": "Fraser Buxton", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24224/"}]}]}], "contributors": [{"name": "Mark Patterson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5064/"}, {"name": "Tamsin Smith", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14108/"}, {"name": "Fraser Buxton", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24224/"}]}