// Numbas version: finer_feedback_settings
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The elements of the transpose of a matrix also swap places following the same rule.</p>\n<p><strong>Example:&nbsp;</strong></p>\n<p>From part b) of the question you have the matrix $M$ given by:</p>\n<p>$M=\\var{Transpose1}.$</p>\n<p>Swapping the rows with the columns (for example meaning the first row becomes the first column in the transpose), gives the answer:</p>\n<p>$M^{T}=\\var{answer}.$</p>\n<p><strong><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/next-steps#Matrices\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></strong></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"matrixdim": {"name": "matrixdim", "group": "matrix notation", "definition": "repeat(random(1..4),2)", "description": "", "templateType": "anything", "can_override": false}, "transpose1": {"name": "transpose1", "group": "matrix notation", "definition": "matrix(repeat(repeat(random(-9..9),matrixdim[1]),matrixdim[0]))", "description": "", "templateType": "anything", "can_override": false}, "squarematrixdim": {"name": "squarematrixdim", "group": "matrix notation", "definition": "random(2..4)", "description": "", "templateType": "anything", "can_override": false}, "squaretranspose": {"name": "squaretranspose", "group": "matrix notation", "definition": "matrix(repeat(repeat(random(-9..9),squarematrixdim),squarematrixdim))", "description": "", "templateType": "anything", "can_override": false}, "answer": {"name": "answer", "group": "matrix notation", "definition": "transpose(transpose1)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "matrixdim[0]<>matrixdim[1]", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "matrix notation", "variables": ["matrixdim", "transpose1", "squarematrixdim", "squaretranspose", "answer"]}], "functions": {"Latexcodebits": {"parameters": [["m", "number"], ["n", "number"]], "type": "list", "language": "jme", "definition": "repeat(repeat('&',n-1)+['\\\\\\\\'],m-1)+[repeat('&',n-1)+['']]"}, "stringify": {"parameters": [["input", "list"]], "type": "string", "language": "javascript", "definition": "var output = '';\nvar i;\nfor (i = 0; i < input.length; i++) {\n  output += input[i];\n} \nreturn output;"}, "Latexcodebitsproductcalc": {"parameters": [["m", "number"], ["k", "number"], ["n", "number"]], "type": "anything", "language": "jme", "definition": "repeat(repeat(repeat('+',k-1)+['&'],n-1)+[repeat('+',k-1)+['\\\\\\\\']],m-1)+[repeat(repeat('+',k-1)+['&'],n-1)+[repeat('+',k-1)+['']]]"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "matrix", "useCustomName": true, "customName": "a)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\var{squaretranspose}$</p>", "correctAnswer": "transpose(squaretranspose)", "correctAnswerFractions": false, "numRows": "2", "numColumns": "2", "allowResize": true, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": "6", "minRows": 1, "maxRows": "6", "prefilledCells": ""}, {"type": "matrix", "useCustomName": true, "customName": "b)", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\var{Transpose1}$</p>", "correctAnswer": "transpose(transpose1)", "correctAnswerFractions": false, "numRows": "2", "numColumns": "2", "allowResize": true, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": "6", "minRows": 1, "maxRows": "6", "prefilledCells": ""}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}], "resources": []}]}], "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Will Morgan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21933/"}]}