// Numbas version: exam_results_page_options
{"name": "Can you multiply these matrices? (same as WBQ 1.28)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Can you multiply these matrices? (same as WBQ 1.28)", "tags": ["matrix multiplication"], "metadata": {"description": "<p>checking by size whether two matrices can be multiplied. Student either gives size of resulting product, or NA if matrices can't be multiplied.</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{F}\\).</p>", "advice": "<p>We can multiply an \\(m\\times k\\) matrix and a \\(k\\times n\\) matrix, i.e. the number of columns of the first matrix and the number of rows of the second matrix have to match. The resulting product has size \\(m\\times n\\).</p>\n<p>\\(A\\) has size \\(3\\times 2\\), \\(E\\) has size \\(3\\times 3\\), so \\(AE\\) does not exist. But \\(EA\\) does exist and has size \\(3\\times 2\\).</p>\n<p>\\(B\\) has size \\(2\\times 2\\), so \\(BE\\) does not exist.</p>\n<p>\\(C\\) has size \\(2\\times 3\\), so \\(CE\\) exists and has size \\(2\\times 3\\).</p>\n<p>\\(D\\) and \\(E\\) both have size \\(3\\times 3\\), so both \\(DE\\) and \\(ED\\) exist and have size \\(3\\times 3\\).</p>", "rulesets": {}, "extensions": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": "matrix([3,0],[-1,2],[1,1])", "description": "", "templateType": "anything"}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "matrix([4,-1],[0,2])", "description": "", "templateType": "anything"}, "C": {"name": "C", "group": "Ungrouped variables", "definition": "matrix([1,4,2],[3,1,5])", "description": "", "templateType": "anything"}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "matrix([1,5,2],[-1,0,1],[3,2,4])", "description": "", "templateType": "anything"}, "F": {"name": "F", "group": "Ungrouped variables", "definition": "matrix([6,1,3],[-1,1,2],[4,1,3])", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["A", "B", "C", "D", "F"], "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>Determine whether the product exists. If the product exists, then enter the size of the result matrix as <code>mxn</code>, using the correct numbers instead of <code>m</code> and <code>n</code>. If the product does not exist, enter <code>NA</code>.</p>\n<p></p>\n<p>\\(AE\\): [[0]]</p>\n<p>\\(EA\\): [[1]]</p>\n<p>\\(BE\\): [[2]]</p>\n<p>\\(CE\\): [[3]]</p>\n<p>\\(DE\\): [[4]]</p>\n<p>\\(ED\\): [[5]]</p>\n<p></p>", "gaps": [{"type": "patternmatch", "useCustomName": true, "customName": "AE", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "NA", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "EA", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": true, "answer": "3 x 2", "displayAnswer": "", "matchMode": "exact"}], "answer": "3x2", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "BE", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "NA", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "CE", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": true, "answer": "2 x 3", "displayAnswer": "", "matchMode": "exact"}], "answer": "2x3", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "DE", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": true, "answer": "3 x 3", "displayAnswer": "", "matchMode": "exact"}], "answer": "3x3", "displayAnswer": "", "matchMode": "exact"}, {"type": "patternmatch", "useCustomName": true, "customName": "ED", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "patternmatch", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "", "useAlternativeFeedback": true, "answer": "3 x 3", "displayAnswer": "", "matchMode": "exact"}], "answer": "3x3", "displayAnswer": "", "matchMode": "exact"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Julia Goedecke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5121/"}]}]}], "contributors": [{"name": "Julia Goedecke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5121/"}]}