// Numbas version: finer_feedback_settings
{"name": "Order of a Matrix, with Subscript Notation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Order of a Matrix, with Subscript Notation", "tags": [], "metadata": {"description": "<p>This question tests understanding of subscript notation for matrices</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<div class=\"content-area\">\n<h1>Subscript Notation</h1>\n<p>Given the matrix:</p>\n$$<br/>\\boldsymbol{M} = \\var{B}<br/>$$</div>\n<div class=\"content-area\"></div>\n<div class=\"content-area\">Answer the following questions.</div>", "advice": "<p><strong>a)</strong></p>\n<p>The order of a matrix is written as $ ROWS \\times COLUMNS$ . In this example there are $\\var{n}$ rows and $\\var{m}$ columns so we would say this matrix has order $\\var{n}\\times\\var{m}$.</p>\n<p></p>\n<p><strong>b)</strong></p>\n<p>$\\boldsymbol{M}_{\\var{n1},\\var{m1}}$ means you are looking for the element in row $\\var{n1}$ and in column $\\var{m1}$. In this case that means we are looking at the element $\\var{E}$.</p>\n<p></p>\n<p><strong>c)</strong></p>\n<p><span data-jme-visible=\"{row_or_col}=0\">The elements of $\\boldsymbol{M}_{\\var{n2},}$ refers to row $\\var{n2}$ of matrix $\\boldsymbol{M}$ as the subscript is written ${\\var{n2},}$ meaning row $\\var{n2}$. Hence we have $\\var{C}$</span></p>\n<p><span data-jme-visible=\"{row_or_col}=1\">The elements of $\\boldsymbol{M}_{,\\var{m2}}$ refers to column $\\var{m2}$ of matrix $\\boldsymbol{M}$ as the subscript is written ${,\\var{m2}}$ meaning column $\\var{m2}$. Hence we have $\\var{C}$</span></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "<p>Rows</p>", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..6)", "description": "<p>columns</p>", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "matrix(repeat(repeat(random(-10..10),m),n))", "description": "", "templateType": "anything", "can_override": false}, "n1": {"name": "n1", "group": "Ungrouped variables", "definition": "random(1..n)", "description": "", "templateType": "anything", "can_override": false}, "m1": {"name": "m1", "group": "Ungrouped variables", "definition": "random(1..m)", "description": "", "templateType": "anything", "can_override": false}, "E": {"name": "E", "group": "Ungrouped variables", "definition": "B[n1-1][m1-1]", "description": "", "templateType": "anything", "can_override": false}, "n2": {"name": "n2", "group": "Ungrouped variables", "definition": "random(1..n)", "description": "", "templateType": "anything", "can_override": false}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "if(row_or_col=0,matrix(B[n2-1]),transpose(matrix(transpose(B)[m2-1])))", "description": "", "templateType": "anything", "can_override": false}, "row_or_col": {"name": "row_or_col", "group": "Ungrouped variables", "definition": "random(0,1)", "description": "", "templateType": "anything", "can_override": false}, "m2": {"name": "m2", "group": "Ungrouped variables", "definition": "random(1..m)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "m", "B", "n1", "m1", "E", "n2", "C", "row_or_col", "m2"], "variable_groups": [], "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>Write down the order of $\\boldsymbol{M}$</p>\n<p style=\"text-align: center;\">[[0]]$\\times$ [[1]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{n}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{M}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "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>State the value of $m_{\\var{n1},\\var{m1}}$</p>\n<p style=\"text-align: center;\">$m_{\\var{n1},\\var{m1}} = $ [[0]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{E}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "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><span data-jme-visible=\"{row_or_col}=0\">Write out the elements of $\\boldsymbol{M}_{\\var{n2},}$</span> <span data-jme-visible=\"{row_or_col}=1\">Write out the elements of $\\boldsymbol{M}_{,\\var{m2}}$</span></p>\n<p style=\"text-align: center;\"><span data-jme-visible=\"{row_or_col}=0\">$\\boldsymbol{M}_{\\var{n2},} = $</span> <span data-jme-visible=\"{row_or_col}=1\">$\\boldsymbol{M}_{,\\var{m2}} = $&nbsp;</span>[[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": "{C}", "correctAnswerFractions": false, "numRows": 1, "numColumns": 1, "allowResize": true, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": "10", "minRows": 1, "maxRows": "10", "prefilledCells": ""}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"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": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}, {"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/"}]}