// Numbas version: finer_feedback_settings
{"name": "Conformable for Multiplication", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Conformable for Multiplication", "tags": [], "metadata": {"description": "<p>This question tests if a students understands when matrices are conformable</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<h1>Conformable Matrices for Multiplication</h1>\n<p>For each of the following pairs of matrices, determine whether they are conformable for multiplication</p>", "advice": "<p>We are asked to determine whether two matrices are conformable for multiplication</p>\n<p>To do this, we must determine the dimensions of each matrix</p>\n<p><strong>a)</strong></p>\n<p>$\\boldsymbol{A}$ has $\\var{n1q1}$ columns and $\\boldsymbol{B}$ has $\\var{m2q1}$ rows</p>\n<div data-jme-visible=\"conf1\">\n<p>Since both of these values are $\\var{n1q1}$, the product $\\boldsymbol{AB}$ is defined and the matrices are conformable</p>\n</div>\n<div data-jme-visible=\"not(conf1)\">\n<p>Since $\\var{n1q1}$ is not equal to $\\var{m2q1}$, the product $\\boldsymbol{AB}$ is not defined and the matrices are not conformable</p>\n</div>\n<p></p>\n<p><strong>b)</strong></p>\n<p>$\\boldsymbol{C}$ has $\\var{n1q2}$ columns and $\\boldsymbol{D}$ has $\\var{m2q2}$ rows</p>\n<div data-jme-visible=\"conf2\">\n<p>Since both of these values are $\\var{n1q2}$, the product $\\boldsymbol{CD}$ is defined and the matrices are conformable</p>\n</div>\n<div data-jme-visible=\"not(conf2)\">\n<p>Since $\\var{n1q2}$ is not equal to $\\var{m2q2}$, the product $\\boldsymbol{CD}$ is not defined and the matrices are not conformable</p>\n</div>\n<p></p>\n<p><strong>c)</strong></p>\n<p>$\\boldsymbol{E}$ has $\\var{n1q3}$ columns and $\\boldsymbol{F}$ has $\\var{m2q3}$ rows</p>\n<div data-jme-visible=\"conf3\">\n<p>Since both of these values are $\\var{n1q3}$, the product $\\boldsymbol{EF}$ is defined and the matrices are conformable</p>\n</div>\n<div data-jme-visible=\"not(conf3)\">\n<p>Since $\\var{n1q3}$ is not equal to $\\var{m2q3}$, the product $\\boldsymbol{AB}$ is not defined and the matrices are not conformable</p>\n</div>\n<p></p>\n<div data-jme-visible=\"not(conf1)\">\n<p></p>\n</div>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"conf1": {"name": "conf1", "group": "q1", "definition": "random(true,false)", "description": "", "templateType": "anything", "can_override": false}, "m1q1": {"name": "m1q1", "group": "q1", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "n1q1": {"name": "n1q1", "group": "q1", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "m2q1": {"name": "m2q1", "group": "q1", "definition": "if(conf1,n1q1,random(1..5))", "description": "", "templateType": "anything", "can_override": false}, "n2q1": {"name": "n2q1", "group": "q1", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "conf2": {"name": "conf2", "group": "q2", "definition": "random(true,false)", "description": "", "templateType": "anything", "can_override": false}, "m1q2": {"name": "m1q2", "group": "q2", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "n1q2": {"name": "n1q2", "group": "q2", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "m2q2": {"name": "m2q2", "group": "q2", "definition": "if(conf2,n1q2,random(1..5))", "description": "", "templateType": "anything", "can_override": false}, "n2q2": {"name": "n2q2", "group": "q2", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "conf3": {"name": "conf3", "group": "q3", "definition": "random(true,false)", "description": "", "templateType": "anything", "can_override": false}, "m1q3": {"name": "m1q3", "group": "q3", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "n1q3": {"name": "n1q3", "group": "q3", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "m2q3": {"name": "m2q3", "group": "q3", "definition": "if(conf3,n1q3,random(1..5))", "description": "", "templateType": "anything", "can_override": false}, "n2q3": {"name": "n2q3", "group": "q3", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "q1", "definition": "transpose(matrix(repeat(repeat(random(0..9),m1q1),n1q1)))", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "q1", "definition": "transpose(matrix(repeat(repeat(random(0..9),m2q1),n2q1)))", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "q2", "definition": "transpose(matrix(repeat(repeat(random(0..9),m1q2),n1q2)))", "description": "", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "q2", "definition": "transpose(matrix(repeat(repeat(random(0..9),m2q2),n2q2)))", "description": "", "templateType": "anything", "can_override": false}, "E": {"name": "E", "group": "q3", "definition": "transpose(matrix(repeat(repeat(random(0..9),m1q3),n1q3)))", "description": "", "templateType": "anything", "can_override": false}, "F": {"name": "F", "group": "q3", "definition": "transpose(matrix(repeat(repeat(random(0..9),m2q3),n2q3)))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "not(conf1 = false and n1q1 = m2q1) and \nnot(conf2 = false and n1q2 = m2q2) and \nnot(conf3 = false and n1q3 = m2q3)", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "q1", "variables": ["conf1", "m1q1", "n1q1", "m2q1", "n2q1", "A", "B"]}, {"name": "q2", "variables": ["conf2", "m1q2", "n1q2", "m2q2", "n2q2", "C", "D"]}, {"name": "q3", "variables": ["conf3", "m1q3", "n1q3", "m2q3", "n2q3", "E", "F"]}], "functions": {}, "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>Consider:</p>\n<p>$$<br/>\\boldsymbol{A} = \\var{A}, \\boldsymbol{B} = \\var{B}<br/>$$</p>\n<p>The product $\\boldsymbol{AB}$ [[0]], and therefore the matrices are [[1]].</p>", "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": "['exists','does not exist']", "matrix": "[if(conf1,1,0),if(conf1,0,1)]"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": "['conformable for multiplication','not conformable for multiplication']", "matrix": "[if(conf1,1,0),if(conf1,0,1)]"}], "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>Consider:</p>\n<p>$$<br/>\\boldsymbol{C} = \\var{C}, \\boldsymbol{D} = \\var{D}<br/>$$</p>\n<p>The product $\\boldsymbol{CD}$ [[0]], and therefore the matrices are [[1]].</p>", "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": "['exists','does not exist']", "matrix": "[if(conf2,1,0),if(conf2,0,1)]"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": "['conformable for multiplication','not conformable for multiplication']", "matrix": "[if(conf2,1,0),if(conf2,0,1)]"}], "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>Consider:</p>\n<p>$$<br/>\\boldsymbol{E} = \\var{E}, \\boldsymbol{F} = \\var{F}<br/>$$</p>\n<p>The product $\\boldsymbol{EF}$ [[0]], and therefore the matrices are [[1]].</p>", "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": "['exists','does not exist']", "matrix": "[if(conf3,1,0),if(conf3,0,1)]"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": "['conformable for multiplication','not conformable for multiplication']", "matrix": "[if(conf3,1,0),if(conf3,0,1)]"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"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": "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/"}]}