// Numbas version: exam_results_page_options
{"name": "Matrix Multiplication 2 (3x3 by 3x2 matrices)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "functions": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Multiplication of $2 \\times 2$ matrices.</p>"}, "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers"]}, "variable_groups": [], "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"], "parts": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "unitTests": [], "customName": "", "gaps": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": "1", "customMarkingAlgorithm": "", "tolerance": 0, "allowResize": false, "customName": "", "markPerCell": false, "showCorrectAnswer": true, "scripts": {}, "correctAnswerFractions": false, "numRows": "2", "numColumns": "2", "type": "matrix", "useCustomName": false, "showFeedbackIcon": true, "correctAnswer": "matrix([\n    [ab11,ab12],\n    [ab21,ab22]\n])", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "allowFractions": false}], "showCorrectAnswer": true, "sortAnswers": false, "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>", "extendBaseMarkingAlgorithm": true, "type": "gapfill", "useCustomName": false, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "marks": 0, "unitTests": [], "customName": "", "gaps": [{"variableReplacementStrategy": "originalfirst", "unitTests": [], "marks": "1", "customMarkingAlgorithm": "", "tolerance": 0, "allowResize": false, "customName": "", "markPerCell": false, "showCorrectAnswer": true, "scripts": {}, "correctAnswerFractions": false, "numRows": "3", "numColumns": "3", "type": "matrix", "useCustomName": false, "showFeedbackIcon": true, "correctAnswer": "matrix([\n    [ba11,ba12,ba13],\n    [ba21,ba22,ba23],\n    [ba31,ba32,ba33]\n])", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "allowFractions": false}], "showCorrectAnswer": true, "sortAnswers": false, "prompt": "<p>$BA = \\begin{pmatrix} \\var{b11}&amp;\\var{b12}\\\\ \\var{b21}&amp;\\var{b22}\\\\ \\var{b31}&amp;\\var{b32}\\end{pmatrix}\\begin{pmatrix} \\var{a11}&amp;\\var{a12}&amp;\\var{a13}\\\\ \\var{a21}&amp;\\var{a22}&amp;\\var{a23}\\\\ \\end{pmatrix}=$ [[0]]</p>", "extendBaseMarkingAlgorithm": true, "type": "gapfill", "useCustomName": false, "showFeedbackIcon": true, "customMarkingAlgorithm": "", "variableReplacements": [], "scripts": {}}], "preamble": {"css": "", "js": ""}, "variables": {"ac22": {"group": "Ungrouped variables", "description": "", "definition": "a21*c12+a22*c22", "name": "ac22", "templateType": "anything"}, "ac12": {"group": "Ungrouped variables", "description": "", "definition": "a11*c12+a12*c22", "name": "ac12", "templateType": "anything"}, "b31": {"group": "Ungrouped variables", "description": "", "definition": "random(-1..1)", "name": "b31", "templateType": "anything"}, "c12": {"group": "Ungrouped variables", "description": "", "definition": "a12+b12", "name": "c12", "templateType": "anything"}, "ab21": {"group": "Ungrouped variables", "description": "", "definition": "a21*b11+a22*b21+a23*b31", "name": "ab21", "templateType": "anything"}, "a11": {"group": "Ungrouped variables", "description": "", "definition": "random(-2,1,2)", "name": "a11", "templateType": "anything"}, "ab11": {"group": "Ungrouped variables", "description": "", "definition": "a11*b11+a12*b21+a13*b31", "name": "ab11", "templateType": "anything"}, "ba32": {"group": "Ungrouped variables", "description": "", "definition": "b31*a12+b32*a22", "name": "ba32", "templateType": "anything"}, "ba31": {"group": "Ungrouped variables", "description": "", "definition": "b31*a11+b32*a21", "name": "ba31", "templateType": "anything"}, "ac11": {"group": "Ungrouped variables", "description": "", "definition": "a11*c11+a12*c21", "name": "ac11", "templateType": "anything"}, "ba13": {"group": "Ungrouped variables", "description": "", "definition": "b11*a13+b12*a23", "name": "ba13", "templateType": "anything"}, "c11": {"group": "Ungrouped variables", "description": "", "definition": "random(1,0,4)", "name": "c11", "templateType": "anything"}, "ba22": {"group": "Ungrouped variables", "description": "", "definition": "b21*a12+b22*a22", "name": "ba22", "templateType": "anything"}, "a12": {"group": "Ungrouped variables", "description": "", "definition": "random(1..4)", "name": "a12", "templateType": "anything"}, "ba12": {"group": "Ungrouped variables", "description": "", "definition": "b11*a12+b12*a22", "name": "ba12", "templateType": "anything"}, "ab22": {"group": "Ungrouped variables", "description": "", "definition": "a21*b12+a22*b22+a23*b32", "name": "ab22", "templateType": "anything"}, "ba33": {"group": "Ungrouped variables", "description": "", "definition": "b31*a13+b32*a23", "name": "ba33", "templateType": "anything"}, "b22": {"group": "Ungrouped variables", "description": "", "definition": "random(-3..-1)", "name": "b22", "templateType": "anything"}, "ba23": {"group": "Ungrouped variables", "description": "", "definition": "b21*a13+b22*a23", "name": "ba23", "templateType": "anything"}, "ba11": {"group": "Ungrouped variables", "description": "", "definition": "b11*a11+b12*a21", "name": "ba11", "templateType": "anything"}, "a23": {"group": "Ungrouped variables", "description": "", "definition": "random(-2..3)", "name": "a23", "templateType": "anything"}, "ac21": {"group": "Ungrouped variables", "description": "", "definition": "a21*c11+a22*c21", "name": "ac21", "templateType": "anything"}, "b11": {"group": "Ungrouped variables", "description": "", "definition": "random(-3,-1,0,3)", "name": "b11", "templateType": "anything"}, "cb12": {"group": "Ungrouped variables", "description": "", "definition": "c11*b12+c12*b22", "name": "cb12", "templateType": "anything"}, "cb11": {"group": "Ungrouped variables", "description": "", "definition": "c11*b11+c12*b21", "name": "cb11", "templateType": "anything"}, "a21": {"group": "Ungrouped variables", "description": "", "definition": "random(-2..2)", "name": "a21", "templateType": "anything"}, "cb22": {"group": "Ungrouped variables", "description": "", "definition": "c21*b12+c22*b22", "name": "cb22", "templateType": "anything"}, "ba21": {"group": "Ungrouped variables", "description": "", "definition": "b21*a11+b22*a21", "name": "ba21", "templateType": "anything"}, "a22": {"group": "Ungrouped variables", "description": "", "definition": "random(1..3)", "name": "a22", "templateType": "anything"}, "b32": {"group": "Ungrouped variables", "description": "", "definition": "random(2..5)", "name": "b32", "templateType": "anything"}, "c22": {"group": "Ungrouped variables", "description": "", "definition": "random(0,1)", "name": "c22", "templateType": "anything"}, "cb21": {"group": "Ungrouped variables", "description": "", "definition": "c21*b11+c22*b21", "name": "cb21", "templateType": "anything"}, "b21": {"group": "Ungrouped variables", "description": "", "definition": "random(2,3)", "name": "b21", "templateType": "anything"}, "c21": {"group": "Ungrouped variables", "description": "", "definition": "random(2..5)", "name": "c21", "templateType": "anything"}, "ab12": {"group": "Ungrouped variables", "description": "", "definition": "a11*b12+a12*b22+a13*b32", "name": "ab12", "templateType": "anything"}, "b12": {"group": "Ungrouped variables", "description": "", "definition": "random(-3..1)", "name": "b12", "templateType": "anything"}, "a13": {"group": "Ungrouped variables", "description": "", "definition": "random(0..2)", "name": "a13", "templateType": "anything"}}, "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>", "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "", "extensions": [], "name": "Matrix Multiplication 2 (3x3 by 3x2 matrices)", "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/"}]}]}], "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/"}]}