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Find the determinant of
\n\\begin{bmatrix}\\var{n11}&\\var{n12}&\\var{n13}\\\\ \\var{n21}&\\var{n22}&\\var{n23}\\\\ \\var{n31} & \\var{n32} & \\var{n33}\\end{bmatrix}
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", "templateType": "randrange"}, "n13": {"name": "n13", "group": "Ungrouped variables", "definition": "random(1 .. 3#1)", "description": "", "templateType": "randrange"}, "n21": {"name": "n21", "group": "Ungrouped variables", "definition": "random(4 .. 5#1)", "description": "", "templateType": "randrange"}, "n22": {"name": "n22", "group": "Ungrouped variables", "definition": "random(1 .. 2#1)", "description": "", "templateType": "randrange"}, "n23": {"name": "n23", "group": "Ungrouped variables", "definition": "random(-9 .. -8#1)", "description": "", "templateType": "randrange"}, "n31": {"name": "n31", "group": "Ungrouped variables", "definition": "random(2 .. 3#1)", "description": "", "templateType": "randrange"}, "n32": {"name": "n32", "group": "Ungrouped variables", "definition": "random(4 .. 5#1)", "description": "", "templateType": "randrange"}, "n33": {"name": "n33", "group": "Ungrouped variables", "definition": "random(1 .. 2#1)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n11", "n12", "n13", "n21", "n22", "n23", "n31", "n32", "n33"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "n11 * (n22*n33-n23*n32)-n12*(n21*n33-n23*n31)+n13*(n21*n32-n22*n31)", "maxValue": "n11 * (n22*n33-n23*n32)-n12*(n21*n33-n23*n31)+n13*(n21*n32-n22*n31)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Demonstration question", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Lisa Mott", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4903/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "Find the determinant of \\begin{bmatrix}1 & 2 &0\\\\ 2 & -1 & 1 \\\\ 1 & -1 & 1 \\end{bmatrix}
", "advice": "To find the determinant of \\begin{bmatrix}1 & 2 & 0 \\\\ 2& -1 & 1 \\\\ 1 & -1 & 1 \\end{bmatrix} if we use the first row,
\n\n$1 \\begin{vmatrix} -1&1\\\\ -1 &1\\end{vmatrix} -1 \\begin{vmatrix}2 & 1\\\\ 1 &1\\end{vmatrix} + 0 \\begin{vmatrix} 2&-1\\\\ 1& -1\\end{vmatrix}$
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", "advice": "Each day, Chris eats {num_apples} apples. There are 7 days in a week.
\n\nTo find the number of apples Chris eats each week, multiply {num_apples} by 7.
\n\nChris eats {7*num_apples} apples per week.
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