// Numbas version: finer_feedback_settings
{"name": "Week 11 (assessed)", "metadata": {"description": "", "licence": "All rights reserved"}, "duration": 0, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "random-subset", "pickQuestions": "1", "questionNames": ["", "", "", ""], "variable_overrides": [[], [], [], []], "questions": [{"name": "subspace q1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Let $V=\\mathbb{R}^2$ be the vector space over $\\mathbb{R}$. For the subset $\\{(a, b) : a, b \\in \\mathbb{Z}\\}$ of $V$, choose all that apply.</p>", "advice": "<p>Do check the lecture notes for details of the subspace test.</p>\n<p>Working through the examples in the lecture notes and the relevant exercises on the problem sheet may also be helpful.&nbsp;</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minMarks": 0, "maxMarks": "2", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "all-or-nothing", "choices": ["It is closed under addition (with regards to the subspace test).", "It is closed under scalar multiplication (with regards to the subspace test).", "It is a subspace.", "It is none of the above."], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "subspace q1b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Let $V=\\mathbb{R}^2$ be the vector space over $\\mathbb{R}$. For the subset $\\{(a, b) : a \\in \\mathbb{Z}, b\\in \\mathbb{R}\\}$ of $V$, choose all that apply.</p>", "advice": "<p>Do check the lecture notes for details of the subspace test.</p>\n<p>Working through the examples in the lecture notes and the relevant exercises on the problem sheet may also be helpful.&nbsp;</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minMarks": 0, "maxMarks": "2", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "all-or-nothing", "choices": ["It is closed under addition (with regards to the subspace test).", "It is closed under scalar multiplication (with regards to the subspace test).", "It is a subspace.", "It is none of the above."], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "subspace q1c", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Let $V=\\mathbb{R}^2$ be the vector space over $\\mathbb{R}$. For the subset $\\{(a, b) : a \\in \\mathbb{R}, b\\in \\mathbb{Q}\\}$ of $V$, choose all that apply.</p>", "advice": "<p>Do check the lecture notes for details of the subspace test.</p>\n<p>Working through the examples in the lecture notes and the relevant exercises on the problem sheet may also be helpful.&nbsp;</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minMarks": 0, "maxMarks": "2", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "all-or-nothing", "choices": ["It is closed under addition (with regards to the subspace test).", "It is closed under scalar multiplication (with regards to the subspace test).", "It is a subspace.", "It is none of the above."], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "subspace q1d", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Let $V=\\mathbb{R}^2$ be the vector space over $\\mathbb{R}$. For the subset $\\{(a, b) : a, b \\in \\mathbb{Q}\\}$ of $V$, choose all that apply.</p>", "advice": "<p>Do check the lecture notes for details of the subspace test.</p>\n<p>Working through the examples in the lecture notes and the relevant exercises on the problem sheet may also be helpful.&nbsp;</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minMarks": 0, "maxMarks": "2", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "all-or-nothing", "choices": ["It is closed under addition (with regards to the subspace test).", "It is closed under scalar multiplication (with regards to the subspace test).", "It is a subspace.", "It is none of the above."], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Group", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "subspace q2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Let $V=\\mathbb{C}$ be the vector space over $\\mathbb{R}$. For the subset $\\mathbb{R}$ of $V$, choose all that apply.</p>", "advice": "<p>Do check the lecture notes for details of the subspace test. Note that the notion of 'over $\\mathbb{F}$' means that the scalars are chosen from $\\mathbb{F}$.</p>\n<p>Working through the examples in the lecture notes and the relevant exercises on the problem sheet may also be helpful.&nbsp;</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minMarks": 0, "maxMarks": "2", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "all-or-nothing", "choices": ["It is closed under addition (with regards to the subspace test).", "It is closed under scalar multiplication (with regards to the subspace test).", "It is a subspace.", "It is none of the above."], "matrix": ["1", "1", "1", 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "subspace q2b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Let $V=\\mathbb{C}$ be the vector space over $\\mathbb{C}$. For the subset $\\mathbb{R}$ of $V$, choose all that apply.</p>", "advice": "<p>Do check the lecture notes for details of the subspace test. Note that the notion of 'over $\\mathbb{F}$' means that the scalars are chosen from $\\mathbb{F}$.</p>\n<p>Working through the examples in the lecture notes and the relevant exercises on the problem sheet may also be helpful.&nbsp;</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minMarks": 0, "maxMarks": "2", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "all-or-nothing", "choices": ["It is closed under addition (with regards to the subspace test).", "It is closed under scalar multiplication (with regards to the subspace test).", "It is a subspace.", "It is none of the above."], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Group", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "subspace q3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Let $V=M_2(\\mathbb{R})$ be the vector space over $\\mathbb{R}$. For the subset of real 2 by 2 matrices with trace equal to one, choose all that apply.</p>", "advice": "<p>Working through the examples in the lecture notes and the relevant exercises on the problem sheet may also be helpful.&nbsp;</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minMarks": 0, "maxMarks": "2", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "all-or-nothing", "choices": ["It is closed under addition (with regards to the subspace test).", "It is closed under scalar multiplication (with regards to the subspace test).", "It is a subspace.", "It is none of the above."], "matrix": [0, 0, 0, "1"], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "subspace q3b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Let $V=M_2(\\mathbb{R})$ be the vector space over $\\mathbb{R}$. For the subset of real 2 by 2 matrices with trace equal to zero, choose all that apply.</p>", "advice": "<p>Working through the examples in the lecture notes and the relevant exercises on the problem sheet may also be helpful.&nbsp;</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minMarks": 0, "maxMarks": "2", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "all-or-nothing", "choices": ["It is closed under addition (with regards to the subspace test).", "It is closed under scalar multiplication (with regards to the subspace test).", "It is a subspace.", "It is none of the above."], "matrix": ["1", "1", "1", 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Group", "pickingStrategy": "random-subset", "pickQuestions": 1, "questionNames": ["", ""], "variable_overrides": [[], []], "questions": [{"name": "subspace q4", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Let $V=M_2(\\mathbb{R})$ be the vector space over $\\mathbb{R}$. For the subset of real 2 by 2 matrices with&nbsp;determinant equal to zero, choose all that apply.</p>", "advice": "<p>Working through the examples in the lecture notes and the relevant exercises on the problem sheet may also be helpful.&nbsp;</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minMarks": 0, "maxMarks": "2", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "all-or-nothing", "choices": ["It is closed under addition (with regards to the subspace test).", "It is closed under scalar multiplication (with regards to the subspace test).", "It is a subspace.", "It is none of the above."], "matrix": [0, "1", 0, 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "subspace q4b", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Let $V=M_2(\\mathbb{R})$ be the vector space over $\\mathbb{R}$. For the subset of real 2 by 2 matrices with determinant equal to one, choose all that apply.</p>", "advice": "<p>Working through the examples in the lecture notes and the relevant exercises on the problem sheet may also be helpful.&nbsp;</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minMarks": 0, "maxMarks": "2", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "all-or-nothing", "choices": ["It is closed under addition (with regards to the subspace test).", "It is closed under scalar multiplication (with regards to the subspace test).", "It is a subspace.", "It is none of the above."], "matrix": [0, "0", 0, "1"], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "which subsets of C^2 are subspaces", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Throughout this question we will work with the vector space $V=\\mathbb{C}^2$ over $\\mathbb{R}$. We let $e_1:=(1, 0)$ and $e_2:=(0,1)\\in \\mathbb{C}^2$.</p>", "advice": "<p>Working through the examples in the lecture notes and the relevant exercises on the problem sheet may also be helpful.&nbsp;</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "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>The set $S_1:=\\{xe_1+iye_1 : x,y \\in \\mathbb{R}\\textrm{ and }xy=0\\}$ is [[0]].</p>\n<p>The set $S_2:=\\{we_1+ize_1 : w,z \\in \\mathbb{C}\\textrm{ and }wz=0\\}$ is [[1]].</p>\n<p>The set $S_3:=\\{xe_1+iye_1 : x,y \\in \\mathbb{R}\\textrm{ and }x^2+y^2=-1\\}$ is [[2]].</p>\n<p>The set $S_4:=\\{xe_1+iye_1 : x,y \\in \\mathbb{R}\\textrm{ with }x^2+y^2=0\\}$ is [[3]].</p>\n<p>The set $S_5:=\\{ze_1+iye_2 : y \\in \\mathbb{R}\\textrm{ and }z \\in \\mathbb{C}\\}$ is [[4]]</p>", "gaps": [{"type": "1_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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": "0", "showCellAnswerState": true, "choices": ["is a subspace of $V$.", "is not a subspace of $V$ as it fails to be non-empty.", "is not a subspace of $V$ as it fails to be closed under addition.", "is not a subspace of $V$ as it fails to be closed under scalar multiplication."], "matrix": [0, 0, "1", 0], "distractors": ["", "", "", ""]}, {"type": "1_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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["is a subspace of $V$.", "is not a subspace of $V$ as it fails to be non-empty.", "is not a subspace of $V$ as it fails to be closed under addition.", "is not a subspace of $V$ as it fails to be closed under scalar multiplication."], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["is a subspace of $V$.", "is not a subspace of $V$ as it fails to be non-empty.", "is not a subspace of $V$ as it fails to be closed under addition.", "is not a subspace of $V$ as it fails to be closed under scalar multiplication."], "matrix": [0, "1", 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["is a subspace of $V$.", "is not a subspace of $V$ as it fails to be non-empty.", "is not a subspace of $V$ as it fails to be closed under addition.", "is not a subspace of $V$ as it fails to be closed under scalar multiplication."], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["is a subspace of $V$.", "is not a subspace of $V$ as it fails to be non-empty.", "is not a subspace of $V$ as it fails to be closed under addition.", "is not a subspace of $V$ as it fails to be closed under scalar multiplication."], "matrix": ["1", 0, 0, 0], "distractors": ["", "", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "dimension questions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>State the dimension of each of the following vector spaces.</p>", "advice": "<p>Consider what a basis might look like in each case. Note how this links to the notion of dimension.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "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>We have, for the following vector spaces over the given fields, that</p>\n<ul>\n<li>$V_1=\\mathbb{R}^2$ over $\\mathbb{R}$ has dimension [[0]].</li>\n<li>$V_2=\\mathbb{C}^2$ over $\\mathbb{R}$ has dimension [[1]].</li>\n<li>$V_3=\\mathbb{C}$ over $\\mathbb{C}$ has dimension [[2]].</li>\n<li>$V_4=M_4(\\mathbb{R})$ over $\\mathbb{R}$ has dimension [[3]].</li>\n<li>$V_5=M_2(\\mathbb{C})$ over $\\mathbb{R}$ has dimension [[4]].</li>\n<li>$V_6=(\\mathbb{F}_2)^3$ over $\\mathbb{F}_2$ has dimension [[5]].</li>\n</ul>\n<p></p>", "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "a number larger than 9 but finite", "infinite"], "matrix": [0, 0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "a number larger than 9 but finite", "infinite"], "matrix": [0, 0, 0, 0, "1", 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "a number larger than 9 but finite", "infinite"], "matrix": [0, "1", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "a number larger than 9 but finite", "infinite"], "matrix": [0, 0, 0, 0, 0, 0, 0, 0, "0", 0, "1", 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "a number larger than 9 but finite", "infinite"], "matrix": [0, 0, 0, 0, 0, 0, 0, 0, "1", 0, "0", 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": true, "choices": ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "a number larger than 9 but finite", "infinite"], "matrix": [0, 0, 0, "1", 0, 0, 0, 0, 0, 0, "0", 0], "distractors": ["", "", "", "", "", "", "", "", "", "", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "Elements in a given span", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Select all of the following functions that are in $\\textrm{span}_\\mathbb{R}\\{1, x, x^2, \\ldots\\}$. (This is a subspace of $F(\\mathbb{R}, \\mathbb{R})$.)</p>", "advice": "<p>The notion of a span involves all linear combinations. These are defined to be finite sums. From this, consider what the set $\\textrm{span}_\\mathbb{R}\\{1, x, x^2, \\ldots\\}$ looks like and what properties elements of this set have. Then consider how we might use these properties to rule out some of the functions below.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "-random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "h": {"name": "h", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}, "e": {"name": "e", "group": "Ungrouped variables", "definition": "random(1..9)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "e", "f", "g", "h"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "minMarks": 0, "maxMarks": "2", "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "all-or-nothing", "choices": ["$\\frac{1}{\\var{a}x^2+\\var{b}x+\\var{c}}$", "$|\\var{d}x+\\var{e}|$", "$\\var{f}$", "$\\var{g}x^{\\var{h}}+1$", "$\\cos(x)$"], "matrix": [0, 0, "1", "1", 0], "distractors": ["", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}, {"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": [""], "variable_overrides": [[]], "questions": [{"name": "subsets of functions are subspaces", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "<p>Let $V=\\{(a_i)_{i\\in \\mathbb{N}} : a_i \\in \\mathbb{R}\\}$ be the set of all real sequences. Select all of the following that are subspaces.</p>", "advice": "<p>Consider how we define the addition and scalar multiplication for this vector space.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "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>The set $S_1$ of real sequences $(a_i)_{i\\in \\mathbb{N}}$ for which there is an $N\\in \\mathbb{N}$ where $a_k=0$ for all $k&gt;N$ [[0]]</p>\n<p>The set $S_2$ of real sequences $(a_i)_{i\\in \\mathbb{N}}$ where $a_i\\le a_{i+1}$ for all $i\\in \\mathbb{N}$ [[1]]</p>\n<p>The subset $S_3$ of $S_1$ which have an even number of non-zero elements [[2]]</p>\n<p>The set $S_4$ of real sequences $(a_i)_{i\\in \\mathbb{N}}$ where $-1&lt;a_i&lt;1$ for every $i\\in \\mathbb{N}$ [[3]]</p>", "gaps": [{"type": "1_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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["is a subspace of $V$.", "is not a subspace of $V$ as it fails to be non-empty.", "is not a subspace of $V$ as it fails to be closed under addition.", "is not a subspace of $V$ as it fails to be closed under scalar multiplication.", "is not a subspace of $V$ as it fails to be closed under addition and fails to be closed under scalar multiplication."], "matrix": ["1", 0, 0, 0, 0], "distractors": ["", "", "", "", ""]}, {"type": "1_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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["is a subspace of $V$.", "is not a subspace of $V$ as it fails to be non-empty.", "is not a subspace of $V$ as it fails to be closed under addition.", "is not a subspace of $V$ as it fails to be closed under scalar multiplication.", "is not a subspace of $V$ as it fails to be closed under addition and fails to be closed under scalar multiplication."], "matrix": [0, "0", 0, "1", "0"], "distractors": ["", "", "", "", ""]}, {"type": "1_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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["is a subspace of $V$.", "is not a subspace of $V$ as it fails to be non-empty.", "is not a subspace of $V$ as it fails to be closed under addition.", "is not a subspace of $V$ as it fails to be closed under scalar multiplication.", "is not a subspace of $V$ as it fails to be closed under addition and fails to be closed under scalar multiplication."], "matrix": ["0", 0, "1", 0, 0], "distractors": ["", "", "", "", ""]}, {"type": "1_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, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["is a subspace of $V$.", "is not a subspace of $V$ as it fails to be non-empty.", "is not a subspace of $V$ as it fails to be closed under addition.", "is not a subspace of $V$ as it fails to be closed under scalar multiplication.", "is not a subspace of $V$ as it fails to be closed under addition and fails to be closed under scalar multiplication."], "matrix": ["0", 0, 0, 0, "1"], "distractors": ["", "", "", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": false, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "navigatemode": "sequence", "onleave": {"action": "none", "message": ""}, "preventleave": true, "typeendtoleave": false, "startpassword": "", "autoSubmit": true, "allowAttemptDownload": true, "downloadEncryptionKey": "", "showresultspage": "review"}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"enterreviewmodeimmediately": false, "showactualmarkwhen": "inreview", "showtotalmarkwhen": "always", "showanswerstatewhen": "inreview", "showpartfeedbackmessageswhen": "inreview", "showexpectedanswerswhen": "never", "showadvicewhen": "inreview", "allowrevealanswer": false, "intro": "<div class=\"vtbegenerated_div\">This is the fourth (and final) assessed quiz for MATH10015 Linear Algebra. It counts for 2.5% of the unit grade. Quizzes should be completed without discussing the questions with other people; of course it is good to use your notes, and it is fine to discuss similar problems with other students.</div>\n<div class=\"vtbegenerated_div\"></div>\n<div class=\"vtbegenerated_div\"></div>\n<div class=\"vtbegenerated_div\">You can attempt this quiz as many times as you like (although questions may change on each attempt). Your score will come from your highest attempt. You should enter your answers as exact numbers unless a question instructs you to give an answer rounded to a certain number of decimal places/significant figures.</div>\n<div class=\"vtbegenerated_div\"></div>\n<div class=\"vtbegenerated_div\"></div>\n<div class=\"vtbegenerated_div\">Clicking on this link will allow you to start a new attempt or resume a previous one. <strong>Please note the deadline.</strong> After you have submitted an attempt you will also see the option to review your answers to that attempt and will be able to see your mark for each question, the correct answer, and solutions for each part. Note that the questions will change for each attempt.</div>\n<div class=\"vtbegenerated_div\"></div>\n<div class=\"vtbegenerated_div\"></div>\n<div class=\"vtbegenerated_div\">Once the deadline has passed you will be able to review your attempts by using the above link.</div>\n<div class=\"vtbegenerated_div\"></div>\n<div class=\"vtbegenerated_div\"></div>\n<div class=\"vtbegenerated_div\">It is recommended that you take a screenshot of this page showing <b>both your name and final score in the same screenshot</b>&nbsp;in case of any technical problems.</div>", "end_message": "", "results_options": {"printquestions": true, "printadvice": true}, "feedbackmessages": [], "reviewshowexpectedanswer": false, "showanswerstate": false, "reviewshowfeedback": true, "showactualmark": false, "showtotalmark": true, "reviewshowscore": true, "reviewshowadvice": true}, "diagnostic": {"knowledge_graph": {"topics": [], "learning_objectives": []}, "script": "diagnosys", "customScript": ""}, "contributors": [{"name": "Charles Garnet Cox", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/24585/"}], "extensions": [], "custom_part_types": [], "resources": []}