// Numbas version: exam_results_page_options
{"name": "Matbis 2 - Bab 2 dan 3 - No 5", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Matbis 2 - Bab 2 dan 3 - No 5", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Diberikan matriks $M=\\begin{bmatrix} \\var{a} &amp; \\var{b} \\\\ \\var{b} &amp; \\var{a} \\end{bmatrix}$.</p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(5..7)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Misal $\\lambda_1$ dan $\\lambda_2$ adalah nilai eigen dari matriks $M$ dengan $\\lambda_1&lt; \\lambda_2$. Maka $\\lambda_1$ dan $\\lambda_2$ berturut-turut adalah $\\ldots$.</p>", "correctAnswer": "matrix([a-b,a+b])", "correctAnswerFractions": true, "numRows": 1, "numColumns": "2", "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": true, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Diketahui $\\mathbf{v}_1 = \\begin{bmatrix} -1 \\\\ a \\end{bmatrix}$ dan $\\mathbf{v}_2 = \\begin{bmatrix} b \\\\ 1 \\end{bmatrix}$ berturut-turut adalah vektor eigen yang berkaitan dengan $\\lambda_1$ dan $\\lambda_2$. Misal $\\mathbf{v} = \\begin{bmatrix} 0 \\\\&nbsp;1 \\end{bmatrix}$. Tentukan $M^{5}\\mathbf{v}$.</p>", "correctAnswer": "matrix([((a+b)^5-(a-b)^5)/2],[((a+b)^5+(a-b)^5)/2])", "correctAnswerFractions": true, "numRows": "2", "numColumns": 1, "allowResize": false, "tolerance": 0, "markPerCell": true, "allowFractions": true, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"type": "m_n_2", "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>Berdasarkan matriks $M$ yang diberikan, pilihlah seluruh pernyataan yang tepat.</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$M = PDP^{-1}$ dengan $P=\\begin{bmatrix} -1 &amp; b \\\\ a &amp; 1 \\end{bmatrix}$ dan $D = \\begin{bmatrix} \\lambda_1 &amp; 0 \\\\ 0 &amp; \\lambda_2 \\end{bmatrix}$.", "$\\det(M) = \\lambda_1\\cdot \\lambda_2$.", "$\\dfrac{1}{\\lambda_1}$ dan $\\dfrac{1}{\\lambda_2}$ merupakan nilai eigen dari $M^{-1}$.", "$M^{-1} = PDP^{-1}$ dengan&nbsp;$P=\\begin{bmatrix} b &amp; -1 \\\\ 1 &amp; a \\end{bmatrix}$ dan $D = \\begin{bmatrix} \\frac{1}{\\lambda_1} &amp; 0 \\\\ 0 &amp; \\frac{1}{\\lambda_2} \\end{bmatrix}$."], "matrix": ["1/3", "1/3", "1/3", "-0.5"], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}]}]}], "contributors": [{"name": "Meong Meong Project", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4687/"}]}