// Numbas version: exam_results_page_options
{"name": "Matrix Multiplication", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Multiplication of $2 \\times 2$ matrices.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "functions": {}, "variable_groups": [], "extensions": [], "ungrouped_variables": ["ba21", "a21", "a22", "ba22", "cb21", "b22", "b21", "cb22", "ac22", "ac21", "ab22", "ab21", "b12", "b11", "c12", "c11", "c22", "a11", "cb11", "cb12", "a12", "c21", "ba11", "ba12", "ab12", "ab11", "ac12", "ac11", "a13", "a23", "b31", "b32", "ba13", "ba23", "ba31", "ba32", "ba33"], "statement": "<p>Do the following matrix problems :<br/>Let <br/>\\[A=\\begin{pmatrix} \\var{a11}&amp;\\var{a12}&amp;\\var{a13}\\\\ \\var{a21}&amp;\\var{a22}&amp;\\var{a23}\\\\ \\end{pmatrix},\\;\\; B=\\begin{pmatrix} \\var{b11}&amp;\\var{b12}\\\\ \\var{b21}&amp;\\var{b22}\\\\ \\var{b31}&amp;\\var{b32}\\end{pmatrix},\\;\\; \\]<br/>Calculate the following products of these matrices:</p>", "preamble": {"css": "", "js": ""}, "name": "Matrix Multiplication", "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "tags": [], "variables": {"ba33": {"templateType": "anything", "description": "", "definition": "b31*a13+b32*a23", "group": "Ungrouped variables", "name": "ba33"}, "ba12": {"templateType": "anything", "description": "", "definition": "b11*a12+b12*a22", "group": "Ungrouped variables", "name": "ba12"}, "b31": {"templateType": "anything", "description": "", "definition": "random(-1..1)", "group": "Ungrouped variables", "name": "b31"}, "a11": {"templateType": "anything", "description": "", "definition": "random(-2,1,2)", "group": "Ungrouped variables", "name": "a11"}, "c12": {"templateType": "anything", "description": "", "definition": "a12+b12", "group": "Ungrouped variables", "name": 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{"templateType": "anything", "description": "", "definition": "c11*b12+c12*b22", "group": "Ungrouped variables", "name": "cb12"}, "b11": {"templateType": "anything", "description": "", "definition": "random(-3,-1,0,3)", "group": "Ungrouped variables", "name": "b11"}, "ac21": {"templateType": "anything", "description": "", "definition": "a21*c11+a22*c21", "group": "Ungrouped variables", "name": "ac21"}, "c22": {"templateType": "anything", "description": "", "definition": "random(0,1)", "group": "Ungrouped variables", "name": "c22"}, "b21": {"templateType": "anything", "description": "", "definition": "random(2,3)", "group": "Ungrouped variables", "name": "b21"}, "cb22": {"templateType": "anything", "description": "", "definition": "c21*b12+c22*b22", "group": "Ungrouped variables", "name": "cb22"}, "ba13": {"templateType": "anything", "description": "", "definition": "b11*a13+b12*a23", "group": "Ungrouped variables", "name": "ba13"}, "ac12": {"templateType": "anything", "description": 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"Ungrouped variables", "name": "b32"}, "c11": {"templateType": "anything", "description": "", "definition": "random(1,0,4)", "group": "Ungrouped variables", "name": "c11"}, "ab22": {"templateType": "anything", "description": "", "definition": "a21*b12+a22*b22+a23*b32", "group": "Ungrouped variables", "name": "ab22"}, "ab21": {"templateType": "anything", "description": "", "definition": "a21*b11+a22*b21+a23*b31", "group": "Ungrouped variables", "name": "ab21"}, "a13": {"templateType": "anything", "description": "", "definition": "random(0..2)", "group": "Ungrouped variables", "name": "a13"}, "ba23": {"templateType": "anything", "description": "", "definition": "b21*a13+b22*a23", "group": "Ungrouped variables", "name": "ba23"}, "b22": {"templateType": "anything", "description": "", "definition": "random(-3..-1)", "group": "Ungrouped variables", "name": "b22"}, "ba11": {"templateType": "anything", "description": "", "definition": "b11*a11+b12*a21", "group": "Ungrouped variables", "name": "ba11"}, "ac22": {"templateType": "anything", "description": "", "definition": "a21*c12+a22*c22", "group": "Ungrouped variables", "name": "ac22"}, "a22": {"templateType": "anything", "description": "", "definition": "random(1..3)", "group": "Ungrouped variables", "name": "a22"}, "a23": {"templateType": "anything", "description": "", "definition": "random(-2..3)", "group": "Ungrouped variables", "name": "a23"}}, "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers"]}, "parts": [{"marks": 0, "unitTests": [], "sortAnswers": false, "scripts": {}, "useCustomName": false, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "prompt": "<p>$AB = \\begin{pmatrix} \\var{a11}&amp;\\var{a12}&amp;\\var{a13}\\\\ \\var{a21}&amp;\\var{a22}&amp;\\var{a23}\\\\ \\end{pmatrix}\\begin{pmatrix} \\var{b11}&amp;\\var{b12}\\\\ \\var{b21}&amp;\\var{b22}\\\\ \\var{b31}&amp;\\var{b32}\\end{pmatrix} = $ [[0]]</p>", "variableReplacements": [], "customName": "", "gaps": [{"marks": 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\\var{a21}&amp;\\var{a22}&amp;\\var{a23}\\\\ \\end{pmatrix}=$ [[0]]</p>", "variableReplacements": [], "customName": "", "gaps": [{"marks": "1", "correctAnswer": "matrix([\n    [ba11,ba12,ba13],\n    [ba21,ba22,ba23],\n    [ba31,ba32,ba33]\n])", "customMarkingAlgorithm": "", "unitTests": [], "correctAnswerFractions": false, "scripts": {}, "useCustomName": false, "markPerCell": false, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "allowResize": false, "allowFractions": false, "tolerance": 0, "variableReplacements": [], "customName": "", "numColumns": "3", "numRows": "3", "showFeedbackIcon": true, "type": "matrix", "extendBaseMarkingAlgorithm": true}], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "type": "gapfill", "extendBaseMarkingAlgorithm": true}], "contributors": [{"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Thomas Waters", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3649/"}]}]}], "contributors": [{"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}, {"name": "Thomas Waters", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3649/"}]}