// Numbas version: exam_results_page_options
{"name": "Matrix multiplication with an indeterminate (WBQ1.35)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Matrix multiplication with an indeterminate (WBQ1.35)", "tags": ["indeterminate", "matrix multiplication"], "metadata": {"description": "<p>Use matrix multiplication to get an equation for \\(k\\) which is then to be solved.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p>We have</p>\n<p style=\"text-align: center;\">\\(\\begin{pmatrix} k &amp; 1 &amp;1\\end{pmatrix}\\var{A}\\begin{pmatrix}k\\\\1\\\\1\\end{pmatrix}= \\begin{pmatrix} k &amp; 1 &amp;1\\end{pmatrix}\\begin{pmatrix}k+1\\\\k+2\\\\-1\\end{pmatrix}\\)</p>\n<p style=\"text-align: center;\">\\(=k(k+1)+k+2-1=k^2+2k+1=(k+1)^2\\).</p>\n<p>So this is zero when \\(k=-1\\).</p>", "rulesets": {}, "extensions": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": " matrix([[1,1,0],[1,0,2],[0,2,-3]])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["A"], "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": [{"label": "Show some steps", "rawLabel": "Show some steps", "otherPart": 1, "variableReplacements": [], "availabilityCondition": "not (answered and credit=1)", "penalty": "", "penaltyAmount": 0, "lockAfterLeaving": false}], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>For which \\(k\\) is</p>\n<p>\\(\\begin{pmatrix} k &amp; 1 &amp;1\\end{pmatrix}\\var{A}\\begin{pmatrix}k\\\\1\\\\1\\end{pmatrix}=0\\)?</p>\n<p>\\(k= \\)[[0]]</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Everything together", "minValue": "-1", "maxValue": "-1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": true, "customName": "Steps", "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 matrix multiplication in two steps:</p>\n<table>\n<tbody>\n<tr style=\"height: 12.4833px;\">\n<td rowspan=\"3\" style=\"height: 44.4833px;\">\\(\\var{A}\\begin{pmatrix}k\\\\1\\\\1\\end{pmatrix} = \\left(\\begin{matrix}\\phantom{.}\\\\\\phantom{.}\\\\\\phantom{.}\\\\\\phantom{.}\\end{matrix}\\right.\\)</td>\n<td style=\"height: 12.4833px;\">[[0]]</td>\n<td rowspan=\"3\" style=\"height: 44.4833px;\">\\(\\left.\\begin{matrix}\\phantom{.}\\\\\\phantom{.}\\\\\\phantom{.}\\\\\\phantom{.}\\end{matrix}\\right)\\)</td>\n</tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px;\">[[1]]</td>\n</tr>\n<tr style=\"height: 16px;\">\n<td style=\"height: 16px;\">[[2]]</td>\n</tr>\n</tbody>\n</table>\n<p>Then calculate \\(\\begin{pmatrix} k &amp; 1 &amp;1\\end{pmatrix} \\) times your answer, to get: [[3]]</p>\n<p>Now set this expression \\(=0\\) and resolve for \\(k\\). \\(k= \\)[[4]]</p>", "gaps": [{"type": "jme", "useCustomName": true, "customName": "Entry 1", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": "Matrix multiplication", "answer": "k+1", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": [{"name": "k", "value": 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