// Numbas version: finer_feedback_settings
{"name": "Matrices: Basics 02", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Matrices: Basics 02", "tags": [], "metadata": {"description": "Identify element of a matrix.", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "<h4 style=\"text-align: left;\">The General Matrix</h4>\n<p style=\"text-align: left;\">A general $m \\times n$ matrix $A$ has $m$ rows and $n$ columns.<br/>The entries in the matrix $A$ are called the elements of $A$.<br/>In matrix $A$ the element in row $i$ and column $j$ is denoted by $a_{ij}$ .</p>", "advice": "<h4>We are presented with random matrices and asked to identify certain elements of those matrices.</h4>\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;\">$c_{\\var{n3}\\var{m3}}$&nbsp;is the element in row $\\var{n3}$ and column $\\var{m3}$. Therefore,&nbsp;&nbsp;$b_{\\var{n2}\\var{m2}}=\\var{E3}$</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">and</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">$c_{\\var{n4}\\var{m4}}$&nbsp;is the element in row $\\var{n4}$ and column $\\var{m4}$. Therefore,&nbsp;&nbsp;$b_{\\var{n2}\\var{m2}}=\\var{E4}$</p>\n<p></p>", "rulesets": {}, "extensions": [], "variables": {"m1": {"name": "m1", "group": "A", "definition": "random(1..2)", "description": "", "templateType": "anything"}, "A": {"name": "A", "group": "A", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n1),m1)))", "description": "", "templateType": "anything"}, "n2": {"name": "n2", "group": "B", "definition": "random(2..4)", "description": "", "templateType": "anything"}, "m2": {"name": "m2", "group": "B", "definition": "random(2..4)", "description": "", "templateType": "anything"}, "B": {"name": "B", "group": "B", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n2),m2)))", "description": "", "templateType": "anything"}, "n3": {"name": "n3", "group": "C", "definition": "random(2..5)", "description": "", "templateType": "anything"}, "m3": {"name": "m3", "group": "C", "definition": "random(2..5)", "description": "", "templateType": "anything"}, "C": {"name": "C", "group": "C", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n3),m3)))", "description": "", "templateType": "anything"}, "n4": {"name": "n4", "group": "D", "definition": "random(1..(n3-1) except n3)", "description": "", "templateType": "anything"}, "m4": {"name": "m4", "group": "D", "definition": "random(1..(m3-1) except m3)", "description": "", "templateType": "anything"}, "n1": {"name": "n1", "group": "A", "definition": "random(1..(m3-1) except m3)", "description": "", "templateType": "anything"}, "D": {"name": "D", "group": "D", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n4),m4)))", "description": "", "templateType": "anything"}, "n5": {"name": "n5", "group": "E", "definition": "m3", "description": "", "templateType": "anything"}, "m5": {"name": "m5", "group": "E", "definition": "n4", "description": "", "templateType": "anything"}, "EE": {"name": "EE", "group": "E", "definition": "transpose(matrix(repeat(repeat(random(-9..9),n5),m5)))", "description": "", "templateType": "anything"}, "e1": {"name": "e1", "group": "A", "definition": "A[n1-1][m1-1]", "description": "", "templateType": "anything"}, "E2": {"name": "E2", "group": "B", "definition": "b[n2-1][m2-1]", "description": "", "templateType": "anything"}, "E3": {"name": "E3", "group": "C", "definition": "c[n3-1][m3-1]", "description": "", "templateType": "anything"}, "E4": {"name": "E4", "group": "C", "definition": "c[n4-1][m4-1]", "description": "", "templateType": "anything"}}, "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": "<h4 style=\"text-align: left;\">Given the matrices:</h4>\n<p style=\"text-align: center;\">&nbsp;$A=\\var{A}$&nbsp; &nbsp; &nbsp;$B=\\var{B}$&nbsp; &nbsp; &nbsp;$C=\\var{C}$</p>\n<p style=\"text-align: center;\"></p>\n<p style=\"text-align: center;\"></p>\n<p style=\"text-align: left;\">&nbsp;Give the values of the following elements of the matrices above:</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">$a_{\\var{n1}\\var{m1}}=$ [[0]]</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">$b_{\\var{n2}\\var{m2}}=$ [[1]]</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">$c_{\\var{n3}\\var{m3}}=$ [[2]]</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">$c_{\\var{n4}\\var{m4}}=$ [[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]", "maxValue": "A[n1-1][m1-1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "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": "b[n2-1][m2-1]", "maxValue": "b[n2-1][m2-1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "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[n3-1][m3-1]", "maxValue": "c[n3-1][m3-1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "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, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "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/"}]}]}], "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}]}