// Numbas version: finer_feedback_settings
{"name": "Representing  A Matrix", "metadata": {"description": "<p>This is a collection of questions to test different aspect to consider when representing a matrix.</p>", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", ""], "variable_overrides": [[], [], []], "questions": [{"name": "Choosing an Element", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "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/"}], "tags": [], "metadata": {"description": "Identify element of a matrix.", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<h1>Finding Elements of a Matrix</h1>\n<p>For each of the given matrices, determine the value of the specific element</p>", "advice": "<p>We are presented with random matrices and asked to identify certain elements of those matrices.</p>\n<p>What you need to remember is:</p>\n<p style=\"text-align: center;\">In matrix $A$ the element in row $i$ and column $j$ is denoted by $a_{ij}$ .</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: left;\">In easier terms, in the subscript the numbers represent <strong>row then column</strong>.&nbsp;</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">So given the matrix&nbsp; $A=\\var{A}$</p>\n<p style=\"text-align: left;\">$a_{\\var{n1}\\var{m1}}$ is the element in row $\\var{n1}$ and column $\\var{m1}$. Therefore,&nbsp; $a_{\\var{n1}\\var{m1}}=\\var{E1}$</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">given the matrix&nbsp; $B=\\var{B}$</p>\n<p style=\"text-align: left;\">$b_{\\var{n2}\\var{m2}}$ is the element in row $\\var{n2}$ and column $\\var{m2}$. Therefore,&nbsp; $b_{\\var{n2}\\var{m2}}=\\var{E2}$</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">given the matrix&nbsp; $C=\\var{C}$</p>\n<p style=\"text-align: left;\">$c_{\\var{n3}\\var{m3}}$ is the element in row $\\var{n3}$ and column $\\var{m3}$. Therefore,&nbsp;&nbsp;$c_{\\var{n3}\\var{m3}}=\\var{E3}$</p>\n<p style=\"text-align: left;\">$c_{\\var{n4}\\var{m4}}$ is the element in row $\\var{n4}$ and column $\\var{m4}$. Therefore,&nbsp;&nbsp;$c_{\\var{n4}\\var{m4}}=\\var{E4}$</p>\n<p></p>", "rulesets": {}, "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", 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"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}, "e1": {"name": "e1", "group": "A", "definition": "A[n1-1][m1-1]", "description": "", "templateType": "anything", "can_override": false}, "E2": {"name": "E2", "group": "B", "definition": "b[n2-1][m2-1]", "description": "", "templateType": "anything", "can_override": false}, "E3": {"name": "E3", "group": "C", "definition": "c[n3-1][m3-1]", "description": "", "templateType": "anything", "can_override": false}, "E4": {"name": "E4", "group": "C", "definition": "c[n4-1][m4-1]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "A", "variables": ["n1", "m1", "A", "e1"]}, {"name": "B", "variables": ["n2", "m2", "B", "E2"]}, {"name": "C", "variables": ["n3", "m3", "C", "E3", "E4"]}, {"name": "D", "variables": ["n4", "m4", "D"]}, {"name": "E", "variables": ["n5", "m5", "EE"]}], "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 style=\"text-align: left;\">Consider the matrices:</p>\n<p style=\"text-align: left;\">$$<br/>A=\\var{A}, \\ \\&nbsp;<br/>B=\\var{B}, \\ \\&nbsp;<br/>C=\\var{C}<br/>$$</p>\n<p style=\"text-align: left;\">Give the values of the following elements:</p>\n<p style=\"text-align: center;\">$a_{\\var{n1}\\var{m1}}=$ [[0]]</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$b_{\\var{n2}\\var{m2}}=$ [[1]]</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$c_{\\var{n3}\\var{m3}}=$ [[2]]</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$c_{\\var{n4}\\var{m4}}=$ [[3]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "A[n1-1][m1-1]", 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"customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "c[n3-1][m3-1]", "maxValue": "c[n3-1][m3-1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "c[n4-1][m4-1]", "maxValue": "c[n4-1][m4-1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Order of a Matrix", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "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/"}], "tags": [], "metadata": {"description": "Classifying matrices (dimensions/order)", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<h1>Order of a Matrix</h1>\n<p>Given the following matrices, determine their dimensions</p>", "advice": "<p style=\"text-align: left;\">A general $m \\times n$ matrix $A$ has $m$ rows and $n$ columns</p>\n<p style=\"text-align: left;\"><strong>a)</strong></p>\n<p style=\"text-align: left;\">$$<br/>A=\\var{A}<br/>$$</p>\n<p style=\"text-align: left;\">$A$ has $\\var{n1}$ rows and $\\var{m1}$ columns. So $A$ has dimensions $ \\var{n1}&nbsp; \\times&nbsp; \\var{m1}$</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\"><strong>b)</strong></p>\n<p style=\"text-align: left;\">$$<br/>B=\\var{B}<br/>$$</p>\n<p style=\"text-align: left;\">$B$ has $\\var{n2}$ rows and $\\var{m2}$ columns. So $B$ has dimensions $ \\var{n2}&nbsp; \\times \\var{m2}$</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\"><strong>c)</strong></p>\n<p style=\"text-align: left;\">$$<br/>C=\\var{C}<br/>$$</p>\n<p style=\"text-align: left;\">$C$ has $\\var{n3}$ rows and $\\var{m3}$ columns. So $C$ has dimensions $ \\var{n3}&nbsp; \\times \\var{m3}$</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\"><strong>d)</strong></p>\n<p style=\"text-align: left;\">$$<br/>D=\\var{D}<br/>$$</p>\n<p style=\"text-align: left;\">$D$ has $\\var{n4}$ rows and $\\var{m4}$ columns. So $D$ has dimensions $ \\var{n4}&nbsp; \\times \\var{m4}$</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\"><strong>e)</strong></p>\n<p style=\"text-align: left;\">$$<br/>E=\\var{EE}<br/>$$</p>\n<p style=\"text-align: left;\">$E$ has $\\var{n5}$ rows and $\\var{m5}$ columns. So $E$ has dimensions $ \\var{n5}&nbsp; \\times \\var{m5}$</p>", "rulesets": {}, "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}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "A", "variables": ["n1", "m1", "A"]}, {"name": "B", "variables": ["n2", "m2", "B"]}, {"name": "C", "variables": ["n3", "m3", "C"]}, {"name": "D", "variables": ["n4", "m4", "D"]}, {"name": "E", "variables": ["n5", "m5", "EE"]}], "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 style=\"text-align: left;\">$$<br/>A=\\var{A}<br/>$$</p>\n<p style=\"text-align: left;\">$A$ is a&nbsp;[[0]]$\\times$ [[1]] matrix.&nbsp;</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{n1}", "maxValue": "{n1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{m1}", "maxValue": "{m1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], 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"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"text-align: left;\">$$<br/>C=\\var{C}<br/>$$</p>\n<p style=\"text-align: left;\">$C$ is a&nbsp;[[0]]$\\times$ [[1]] matrix.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{n3}", "maxValue": "{n3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": 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"originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"text-align: left;\">$$<br/>D=\\var{D}<br/>$$</p>\n<p style=\"text-align: left;\">$D$ is a [[0]]$\\times$ [[1]] matrix.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{n4}", "maxValue": "{n4}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, 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"adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p style=\"text-align: left;\">$$<br/>E=\\var{EE}<br/>$$</p>\n<p style=\"text-align: left;\">$E$ is a [[0]]$\\times$ [[1]] matrix.</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{n5}", "maxValue": "{n5}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, 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[{"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/"}], "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": {}, "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}", 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"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, 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