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{"name": "Matrices: Basics 01", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Matrices: Basics 01", "tags": [], "metadata": {"description": "Classifying matrices (dimensions/order)", "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 \"classify\" them.&nbsp;</h4>\n<p>This simply means \"give their dimensions\" - how many rows and columns do they have?</p>\n<p>In mathematical language you need to know that:</p>\n<p style=\"text-align: center;\">A general $m \\times n$ matrix $A$ has $m$ rows and $n$ columns.</p>\n<p>In simpler terms, the size is ALWAYS given as:</p>\n<p style=\"text-align: center;\">$\\Large ROWS \\times COLUMNS $</p>\n<p style=\"text-align: left;\"></p>\n<p style=\"text-align: left;\">Once you remember this, these are very straightforward.</p>\n<p style=\"text-align: left;\">&nbsp;&nbsp;</p>\n<p style=\"text-align: left;\">$A=\\var{A}$&nbsp; &nbsp; &nbsp;$A$ has $\\var{n1}$ rows and $\\var{m1}$ columns. So $A$ has dimensions $&nbsp;\\var{n1}&nbsp; \\times&nbsp; \\var{m1}$</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">$B=\\var{B}$&nbsp; &nbsp; &nbsp;$B$ has $\\var{n2}$ rows and $\\var{m2}$ columns. So $B$ has dimensions $&nbsp;\\var{n2}&nbsp; \\times&nbsp;\\var{m2}$</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">$C=\\var{C}$&nbsp; &nbsp; &nbsp;$C$ has $\\var{n3}$ rows and $\\var{m3}$ columns. So $C$ has dimensions $&nbsp;\\var{n3}&nbsp; \\times&nbsp;\\var{m3}$</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">$D=\\var{D}$&nbsp; &nbsp; &nbsp;$D$ has $\\var{n4}$ rows and $\\var{m4}$ columns. So $D$ has dimensions $&nbsp;\\var{n4}&nbsp; \\times&nbsp;\\var{m4}$</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: left;\">$E=\\var{EE}$&nbsp; &nbsp; &nbsp;$E$ has $\\var{n5}$ rows and $\\var{m5}$ columns. So $E$ has dimensions $&nbsp;\\var{n5}&nbsp; \\times&nbsp;\\var{m5}$</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": 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"description": "", "templateType": "anything"}}, "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": "<h4 style=\"text-align: left;\">Classify the following matrices:</h4>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p style=\"text-align: center;\">$A=\\var{A}$</p>\n<p style=\"text-align: center;\">$A$ is a&nbsp;[[0]]$\\times$ [[1]] matrix.</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$B=\\var{B}$</p>\n<p style=\"text-align: center;\">$B$ is a&nbsp;[[2]]$\\times$ [[3]] matrix.</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$C=\\var{C}$</p>\n<p style=\"text-align: center;\">$C$ is a&nbsp;[[4]]$\\times$ [[5]] matrix.</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$D=\\var{D}$</p>\n<p style=\"text-align: center;\">$D$ is a [[6]]$\\times$ [[7]] matrix.</p>\n<p style=\"text-align: center;\">&nbsp;</p>\n<p style=\"text-align: center;\">$E=\\var{EE}$</p>\n<p style=\"text-align: center;\">$E$ is a [[8]]$\\times$ [[9]] matrix.</p>\n<p style=\"text-align: center;\">&nbsp;</p>", "gaps": 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