// Numbas version: finer_feedback_settings
{"name": "Finding the Transpose", "extensions": [], "custom_part_types": [], "resources": [["question-resources/Tran_Mat.gif", "/srv/numbas/media/question-resources/Tran_Mat.gif"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Finding the Transpose", "tags": [], "metadata": {"description": "Transpose of a matrix", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<h1>The Transpose of a Matrix</h1>\n<p>For each of the given matrices, give the transpose</p>\n<p><em>You will have to define the dimension of the transposed matrix before you enter your answer.</em></p>", "advice": "<p>The transposition process results in rows becoming columns and columns becoming rows.</p>\n<p>It may help to imagine the matrix being \"flipped\" about its diagonal.</p>\n<p style=\"text-align: center;\"><img src=\"resources/question-resources/Tran_Mat.gif\"/></p>\n<p style=\"text-align: left;\">Using this technique gives us:</p>\n<p style=\"text-align: left;\"><strong>a)</strong></p>\n<p style=\"text-align: left;\">$$<br/>A=\\var{A} \\;\\;\\; A^{T}=\\var{TA}<br/>$$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>\n<p style=\"text-align: left;\"><strong>b)</strong></p>\n<p style=\"text-align: left;\">$$<br/>B=\\var{B} \\;\\;\\; B^{T}=\\var{TB}<br/>$$</p>\n<p style=\"text-align: left;\"><strong>c)</strong></p>\n<p style=\"text-align: left;\">$$<br/>C=\\var{C} \\;\\;\\; C^{T}=\\var{TC}<br/>$$</p>\n<p style=\"text-align: left;\"><strong>d)</strong></p>\n<p style=\"text-align: left;\">$$<br/>D=\\var{D} \\;\\;\\; D^{T}=\\var{TD}<br/>$$</p>\n<p style=\"text-align: left;\"><strong>e)</strong></p>\n<p style=\"text-align: left;\">$$<br/>E=\\var{EE} \\;\\;\\; E^{T}=\\var{TE}<br/>$$&nbsp; &nbsp; &nbsp;</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"m1": {"name": "m1", "group": "A", "definition": "random(1..2)", "description": "", "templateType": "anything", "can_override": false}, "A": {"name": "A", "group": "A", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n1),m1)))", "description": "", "templateType": "anything", "can_override": false}, "n2": {"name": "n2", "group": "B", "definition": "random(2..4)", "description": "", "templateType": "anything", "can_override": false}, "m2": {"name": "m2", "group": "B", "definition": "random(2..4)", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "B", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n2),m2)))", "description": "", "templateType": "anything", "can_override": false}, "n3": {"name": "n3", "group": "C", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "m3": {"name": "m3", "group": "C", "definition": "random(2..5)", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "C", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n3),m3)))", "description": "", "templateType": "anything", "can_override": false}, "n4": {"name": "n4", "group": "D", "definition": "random(1..(n3-1) except n3)", "description": "", "templateType": "anything", "can_override": false}, "m4": {"name": "m4", "group": "D", "definition": "random(1..(m3-1) except m3)", "description": "", "templateType": "anything", "can_override": false}, "n1": {"name": "n1", "group": "A", "definition": "random(1..(m3-1) except m3)", "description": "", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "D", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n4),m4)))", "description": "", "templateType": "anything", "can_override": false}, "n5": {"name": "n5", "group": "E", "definition": "m3", "description": "", "templateType": "anything", "can_override": false}, "m5": {"name": "m5", "group": "E", "definition": "n4", "description": "", "templateType": "anything", "can_override": false}, "EE": {"name": "EE", "group": "E", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n5),m5)))", "description": "", "templateType": "anything", "can_override": false}, "TA": {"name": "TA", "group": "A", "definition": "transpose(A)", "description": "", "templateType": "anything", "can_override": false}, "TB": {"name": "TB", "group": "B", "definition": "transpose(B)", "description": "", "templateType": "anything", "can_override": false}, "TC": {"name": "TC", "group": "C", "definition": "transpose(C)", "description": "", "templateType": "anything", "can_override": false}, "TD": {"name": "TD", "group": "D", "definition": "transpose(D)", "description": "", "templateType": "anything", "can_override": false}, "TE": {"name": "TE", "group": "E", "definition": "transpose(EE)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "A", "variables": ["n1", "m1", "A", "TA"]}, {"name": "B", "variables": ["n2", "m2", "B", "TB"]}, {"name": "C", "variables": ["n3", "m3", "C", "TC"]}, {"name": "D", "variables": ["n4", "m4", "D", "TD"]}, {"name": "E", "variables": ["n5", "m5", "EE", "TE"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Let:</p>\n<p>$$<br/>A=\\var{A}<br/>$$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>\n<p>Find $A^{T}$</p>\n<p style=\"text-align: center;\">$A^{T}=$ [[0]]</p>", "gaps": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "{TA}", "correctAnswerFractions": false, "numRows": 1, "numColumns": 1, "allowResize": true, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}], "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>Let:</p>\n<p>$$<br/>B=\\var{B}<br/>$$</p>\n<p>Find $B^{T}$</p>\n<p style=\"text-align: center;\">$B^{T}=$ [[0]]</p>", "gaps": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "{TB}", "correctAnswerFractions": false, "numRows": 1, "numColumns": 1, "allowResize": true, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}], "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>Let:</p>\n<p>$$<br/>C=\\var{C}<br/>$$</p>\n<p>Find $C^{T}$</p>\n<p style=\"text-align: center;\">$C^{T}=$ [[0]]</p>", "gaps": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "{TC}", "correctAnswerFractions": false, "numRows": 1, "numColumns": 1, "allowResize": true, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}], "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>Let:</p>\n<p>$$<br/>D=\\var{D}<br/>$$</p>\n<p>Find $D^{T}$</p>\n<p style=\"text-align: center;\">$D^{T}=$ [[0]]</p>", "gaps": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "{TD}", "correctAnswerFractions": false, "numRows": 1, "numColumns": 1, "allowResize": true, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}], "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>Let:</p>\n<p>$$<br/>E=\\var{EE}<br/>$$&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</p>\n<p>Find $E^{T}$&nbsp;</p>\n<p style=\"text-align: center;\">$E^{T}=$ [[0]]</p>", "gaps": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "{TE}", "correctAnswerFractions": false, "numRows": 1, "numColumns": 1, "allowResize": true, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"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": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"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/"}]}