// Numbas version: exam_results_page_options
{"name": "Sums of matrices (same as WBQ 1.22)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Sums of matrices (same as WBQ 1.22)", "tags": ["matrix addition", "matrix sum"], "metadata": {"description": "<p>simple sums of matrices and scalar mult of matrices.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Let \\(A=\\var{A}\\), \\(B=\\var{B}\\), \\(C=\\var{C}\\), \\(D=\\var{D}\\), \\(E=\\var{G}\\), \\(F=\\var{F}\\), and \\(\\lambda=\\var{lambda}\\).</p>", "advice": "<p>We can add matrices which have the same size, so the same number of rows and columns. So \\(A\\) and \\(B\\) match together, \\(C\\) and \\(D\\), and \\(E\\) and \\(F\\). We can also add any matrix to itself.</p>\n<p>When we add matrices, we add entry by entry. You can see the answers revealed above. (You may have to click back to the relevant part with the menu at the top.)</p>\n<p>Any matrix can be multiplied by a scalar: every entry is multiplied individually by the scalar. You can see the answers revealed above.</p>", "rulesets": {}, "extensions": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": "matrix([-1,2],[0,1])", "description": "", "templateType": "anything"}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "matrix([1,3],[-1,2])", "description": "", "templateType": "anything"}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "matrix([0,1,-2],[1,2,3])", "description": "", "templateType": "anything"}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "matrix([0,0,0],[0,0,0])", "description": "", "templateType": "anything"}, "G": {"name": "G", "group": "Ungrouped variables", "definition": "vector(1,-3,-3)", "description": "", "templateType": "anything"}, "F": {"name": "F", "group": "Ungrouped variables", "definition": "vector(-1,3,2)", "description": "", "templateType": "anything"}, "lambda": {"name": "lambda", "group": "Ungrouped variables", "definition": "3", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": "100"}, "ungrouped_variables": ["A", "B", "C", "D", "G", "F", "lambda"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": true, "customName": "Which sums are possible?", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Calculate the sums", "rawLabel": "", "otherPart": 1, "variableReplacements": [], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": true}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Which of the following sums are possible? If e.g. <span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"MathJax\" id=\"MathJax-Element-104-Frame\" style=\"position: relative;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;\" role=\"presentation\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-363\" style=\"width: 3.364em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.755em; height: 0px; font-size: 121%;\"><span style=\"position: absolute; clip: rect(1.433em, 1002.75em, 2.561em, -1000em); top: -2.314em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-364\"><span class=\"mi\" id=\"MathJax-Span-365\" style=\"font-family: MathJax_Math; font-style: italic;\">A</span><span class=\"mo\" id=\"MathJax-Span-366\" style=\"font-family: MathJax_Main; padding-left: 0.222em;\">+</span><span class=\"mi\" id=\"MathJax-Span-367\" style=\"font-family: MathJax_Math; font-style: italic; padding-left: 0.222em;\">B</span></span><span style=\"display: inline-block; width: 0px; height: 2.314em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.166em; border-left: 0px solid; width: 0px; height: 1.099em;\"></span></span></nobr></span> is possible, select the tick-box in row <span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"MathJax\" id=\"MathJax-Element-105-Frame\" style=\"position: relative;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;\" role=\"presentation\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-368\" style=\"width: 0.939em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 0.771em; height: 0px; font-size: 121%;\"><span style=\"position: absolute; clip: rect(1.433em, 1000.75em, 2.479em, -1000em); top: -2.314em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-369\"><span class=\"mi\" id=\"MathJax-Span-370\" style=\"font-family: MathJax_Math; font-style: italic;\">A</span></span><span style=\"display: inline-block; width: 0px; height: 2.314em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.067em; border-left: 0px solid; width: 0px; height: 1em;\"></span></span></nobr></span> and column <span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"MathJax\" id=\"MathJax-Element-106-Frame\" style=\"position: relative;\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/math&gt;\" role=\"presentation\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-371\" style=\"width: 0.939em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 0.771em; height: 0px; font-size: 121%;\"><span style=\"position: absolute; clip: rect(1.466em, 1000.77em, 2.479em, -1000em); top: -2.314em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-372\"><span class=\"mi\" id=\"MathJax-Span-373\" style=\"font-family: MathJax_Math; font-style: italic;\">B</span></span><span style=\"display: inline-block; width: 0px; height: 2.314em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.067em; border-left: 0px solid; width: 0px; height: 0.96em;\"></span></span></nobr></span>. You will receive one mark for a correct answer and -1 for an incorrect answer.</p>\n<p>[[0]]</p>", "gaps": [{"type": "m_n_x", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Which matrices can be added", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": false, "displayType": "checkbox", "warningType": "none", "showCellAnswerState": true, "choices": ["\\(A\\)", "\\(B\\)", "\\(C\\)", "\\(D\\)", "\\(E\\)", "\\(F\\)"], "matrix": [["1", "1", "-1", "-1", "-1", "-1"], ["1", "1", "-1", "-1", "-1", "-1"], ["-1", "-1", "1", "1", "-1", "-1"], ["-1", "-1", "1", "1", "-1", "-1"], ["-1", "-1", "-1", "-1", "1", "1"], ["-1", "-1", "-1", "-1", "1", "1"]], "layout": {"type": "uppertriangle", "expression": ""}, "answers": ["\\(A\\)", "\\(B\\)", "\\(C\\)", "\\(D\\)", "\\(E\\)", "\\(F\\)"]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Calculate the sums", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [{"label": "Scalar multiplication", "rawLabel": "", "otherPart": 2, "variableReplacements": [], "availabilityCondition": "answered", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Here are some of the matrix sums that are possible (but not all). Calculate these sums.</p>\n<p>\\(A+B= \\) [[0]]</p>\n<p>\\(C+D= \\) [[1]]</p>\n<p>\\(E+F= \\) [[2]]</p>", "gaps": [{"type": "matrix", "useCustomName": true, "customName": "A+B", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Adding matrices", "correctAnswer": "{A+B}", "correctAnswerFractions": false, "numRows": "2", "numColumns": "2", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"type": "matrix", "useCustomName": true, "customName": "C+D", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, 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"allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Scalar multiplication", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate the following scalar multiplications:</p>\n<p>\\(\\lambda B = \\) [[0]]</p>\n<p>\\(\\lambda C = \\) [[1]]</p>\n<p>\\(\\lambda D= \\) [[2]]</p>\n<p>\\(\\lambda E= \\) [[3]]</p>", "gaps": [{"type": "matrix", "useCustomName": true, "customName": "lambda B", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": 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