// Numbas version: exam_results_page_options
{"name": "Adding 2x2 matrices", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Adding 2x2 matrices", "tags": [], "metadata": {"description": "<p>Adding 2x2 matrices. Very simple question. Marks per correct entry.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p>To add matrices, we add each entry separately: entry 1,1 of the first matrix plus entry 1,1 of the second matrix goes into entry 1,1 of the sum, and so on.</p>\n<p>\\[\\begin{pmatrix}\\simplify[]{{a11}+{b11}} &amp; \\var{a12}+\\var{b12} \\\\ \\var{a21} + \\var{b21} &amp; \\var{a22}+\\var{b22}\\end{pmatrix}= \\begin{pmatrix} \\var{c11} &amp; \\var{c12} \\\\ \\var{c21} &amp; \\var{c22}\\end{pmatrix}\\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"c12": {"name": "c12", "group": "Ungrouped variables", "definition": "a12+b12", "description": "", "templateType": "anything", "can_override": false}, "a21": {"name": "a21", "group": "Ungrouped variables", "definition": "random(-4 .. 4#1)", "description": "", "templateType": "randrange", "can_override": false}, "c11": {"name": "c11", "group": "Ungrouped variables", "definition": "a11+b11", "description": "", "templateType": "anything", "can_override": false}, "a22": {"name": "a22", "group": "Ungrouped variables", "definition": "random(-5 .. 5#1)", "description": "", "templateType": "randrange", "can_override": false}, "b12": {"name": "b12", "group": "Ungrouped variables", "definition": "random(-2 .. 2#1)", "description": "", "templateType": "randrange", "can_override": false}, "b21": {"name": "b21", "group": "Ungrouped variables", "definition": "random(-5 .. 5#1)", "description": "", "templateType": "randrange", "can_override": false}, "a11": {"name": "a11", "group": "Ungrouped variables", "definition": "random(-3 .. 3#1)", "description": "", "templateType": "randrange", "can_override": false}, "c22": {"name": "c22", "group": "Ungrouped variables", "definition": "a22+b22", "description": "", "templateType": "anything", "can_override": false}, "c21": {"name": "c21", "group": "Ungrouped variables", "definition": "a21+b21", "description": "", "templateType": "anything", "can_override": false}, "b11": {"name": "b11", "group": "Ungrouped variables", "definition": "random(-5 .. 5#1)", "description": "", "templateType": "randrange", "can_override": false}, "b22": {"name": "b22", "group": "Ungrouped variables", "definition": "random(-2 .. 2#1)", "description": "", "templateType": "randrange", "can_override": false}, "a12": {"name": "a12", "group": "Ungrouped variables", "definition": "random(-3 .. 3#1)", "description": "", "templateType": "randrange", "can_override": false}, "matrixC": {"name": "matrixC", "group": "Ungrouped variables", "definition": "matrix([c11,c12],[c21,c22])", "description": "<p>Matrix C, the sum of matrices A and B.</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "(a11*a12*a21*a22<>0) and(b11*b12*b21*b22<>0)", "maxRuns": 100}, "ungrouped_variables": ["a11", "a12", "a21", "a22", "b11", "b12", "b21", "b22", "c11", "c12", "c21", "c22", "matrixC"], "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>Calculate \\(\\left( \\begin{array}{ccc}<br/>\\var{a11} &amp; \\var{a12} \\\\<br/>\\var{a21} &amp; \\var{a22} \\end{array} \\right)+\\left( \\begin{array}{ccc}<br/>\\var{b11} &amp; \\var{b12} \\\\<br/>\\var{b21} &amp; \\var{b22}&nbsp; \\end{array} \\right)=\\) [[0]].</p>\n<p></p>", "gaps": [{"type": "matrix", "useCustomName": true, "customName": "Gap 0", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "matrixC", "correctAnswerFractions": false, "numRows": "2", "numColumns": "2", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Tatiana Tyukina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/341/"}, {"name": "Julia Goedecke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5121/"}]}]}], "contributors": [{"name": "Tatiana Tyukina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/341/"}, {"name": "Julia Goedecke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5121/"}]}