// Numbas version: exam_results_page_options
{"name": "Ex 1 Linear combinations of 2 x 2 matrices draft 2", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"preamble": {"css": "", "js": ""}, "tags": [], "variables": {"q": {"name": "q", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-6..6 except [0,1,-1,p])", "description": "<p>constant multiple of matrix B to combine with multiple of A</p>"}, "c": {"name": "c", "group": "Ungrouped variables", "templateType": "anything", "definition": "matrix(repeat(repeat(random(-5..5 except [0,a[0][0],b[0][0]]),2),2))", "description": "<p>randomly generated 2x2 matrix, different to A and B</p>"}, "r1": {"name": "r1", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-6..6 except [0,1,-1,p1,q1])", "description": "<p>constant multiple of matrix C (to combine with A and B)</p>"}, "b": {"name": "b", "group": "Ungrouped variables", "templateType": "anything", "definition": "matrix(repeat(repeat(random(-5..5 except [0,a[0][0]]),2),2))", "description": "<p>randomly generated 2x2 matrix (different to A)</p>"}, "linear_combination_a_b_and_c": {"name": "linear_combination_a_b_and_c", "group": "Ungrouped variables", "templateType": "anything", "definition": "p1*a+q1*b+r1*c", "description": ""}, "a_plus_b": {"name": "a_plus_b", "group": "Ungrouped variables", "templateType": "anything", "definition": "a+b", "description": ""}, "p1": {"name": "p1", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..6 except p)", "description": "<p>constant multiple of matrix A (to combine with B and C)</p>"}, "a": {"name": "a", "group": "Ungrouped variables", "templateType": "anything", "definition": "matrix(repeat(repeat(random(-5..5 except 0),2),2))", "description": "<p>randomly generated 2x2 matrix</p>"}, "q1": {"name": "q1", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(-6..6 except [0,1,-1,p1,q])", "description": "<p>constant multiple of matrix B (to combine with A and C)</p>"}, "linear_combination_a_and_b": {"name": "linear_combination_a_and_b", "group": "Ungrouped variables", "templateType": "anything", "definition": "p*a+q*b", "description": ""}, "p": {"name": "p", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..6)", "description": "<p>constant multiple of matrix A</p>"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noleadingminus"]}, "extensions": ["stats"], "functions": {}, "advice": "", "metadata": {"description": "<p>Linear combinations of $2 \\times 2$ matrices. Three examples.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "ungrouped_variables": ["a", "q1", "c", "b", "r1", "q", "p", "p1", "a_plus_b", "linear_combination_a_and_b", "linear_combination_a_b_and_c"], "variable_groups": [], "name": "Ex 1 Linear combinations of 2 x 2 matrices draft 2", "parts": [{"adaptiveMarkingPenalty": 0, "unitTests": [], "customMarkingAlgorithm": "", "customName": "", "prompt": "<p>$\\mathrm{A}$+$\\mathrm{B}$ =&nbsp; [[0]]</p>", "marks": 0, "gaps": [{"numRows": "2", "adaptiveMarkingPenalty": 0, "markPerCell": false, "unitTests": [], "customMarkingAlgorithm": "", "customName": "", "tolerance": 0, "marks": "0.2", "correctAnswer": "a_plus_b", "useCustomName": false, "correctAnswerFractions": false, "numColumns": "2", "allowResize": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "type": "matrix", "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": [], "allowFractions": false}], "useCustomName": false, "sortAnswers": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": []}, {"adaptiveMarkingPenalty": 0, "unitTests": [], "customMarkingAlgorithm": "", "customName": "", "prompt": "<p>$\\simplify{{p}A+{q}B} = $ [[0]]</p>", "marks": 0, "gaps": [{"numRows": "2", "adaptiveMarkingPenalty": 0, "markPerCell": false, "unitTests": [], "customMarkingAlgorithm": "", "customName": "", "tolerance": 0, "marks": "0.4", "correctAnswer": "linear_combination_a_and_b", "useCustomName": false, "correctAnswerFractions": false, "numColumns": "2", "allowResize": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "type": "matrix", "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": [], "allowFractions": false}], "useCustomName": false, "sortAnswers": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": []}, {"adaptiveMarkingPenalty": 0, "unitTests": [], "customMarkingAlgorithm": "", "customName": "", "prompt": "<p>$\\simplify{{p1}A+{q1}B+{r1}C}=$ [[0]]</p>", "marks": 0, "gaps": [{"numRows": "2", "adaptiveMarkingPenalty": 0, "markPerCell": false, "unitTests": [], "customMarkingAlgorithm": "", "customName": "", "tolerance": 0, "marks": "0.6", "correctAnswer": "linear_combination_a_b_and_c", "useCustomName": false, "correctAnswerFractions": false, "numColumns": "2", "allowResize": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "type": "matrix", "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": [], "allowFractions": false}], "useCustomName": false, "sortAnswers": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "showCorrectAnswer": true, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": []}], "statement": "<p>Let&nbsp;<br/>\\[A=\\simplify{{a}},\\;\\; B=\\simplify{{b}},\\;\\; C=\\simplify{{c}}\\]<br/>Calculate the following $2 \\times 2$ matrices:</p>\n<p>&nbsp;</p>", "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}]}], "contributors": [{"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}