// Numbas version: finer_feedback_settings
{"name": "Vectors - Introductory exercise (WB Q1.1 randomised)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Vectors - Introductory exercise (WB Q1.1 randomised)", "tags": [], "metadata": {"description": "<p>Simple vector addition and scalar multiplication in \\(\\mathbb{R}^2\\).</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Calculate the following:</p>", "advice": "<p>We add vectors entry by entry, and we multiply a vector by a scalar by multiplying each entry.</p>\n<p><strong>Part a) </strong>Zero times any vector is the zero vector: \\(0\\cdot \\begin{pmatrix}x_1\\\\x_2\\end{pmatrix}=\\begin{pmatrix}0\\\\0\\end{pmatrix}\\).</p>\n<p><strong>Part b) </strong>\\[\\var{v1}+\\var{v2}=\\begin{pmatrix}\\simplify[]{{v1[0]}+{v2[0]}} \\\\ \\simplify[]{{v1[1]}+{v2[1]}}&nbsp; \\end{pmatrix} = \\var{v1+v2}\\]</p>\n<p><strong>Part c) </strong>\\[\\var{mu1}\\begin{pmatrix}\\sqrt{\\var{n}}\\\\\\var{w1[1]}\\end{pmatrix}+\\var{mu2}\\begin{pmatrix}-\\frac{\\sqrt{\\var{n}}}{\\var{b}}\\\\\\var{w2[1]}\\end{pmatrix}=\\begin{pmatrix}\\var{mu1}\\sqrt{\\var{n}}-\\var{mu2}\\frac{\\sqrt{\\var{n}}}{\\var{b}}\\\\\\var{mu1}\\var{w1[1]}+\\var{mu2}\\var{w2[1]}\\end{pmatrix} = \\var{mu1*w1+mu2*w2}\\]</p>", "rulesets": {}, "extensions": [], "variables": {"v1": {"name": "v1", "group": "Ungrouped variables", "definition": "vector((repeat(random(1..5),2)))", "description": "", "templateType": "anything"}, "v2": {"name": "v2", "group": "Ungrouped variables", "definition": "vector((repeat(random(1..5),2)))", "description": "", "templateType": "anything"}, "w1": {"name": "w1", "group": "Ungrouped variables", "definition": "vector(sqrt(n),pi)", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", 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[], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<table>\n<tbody>\n<tr>\n<td rowspan=\"2\">\\(0\\cdot \\begin{pmatrix}x_1\\\\x_2\\end{pmatrix}= \\left( \\begin{matrix}\\phantom{.}\\\\\\phantom{.}\\\\\\phantom{.}\\end{matrix}\\right.\\)</td>\n<td>[[0]]</td>\n<td rowspan=\"2\">\\(\\left.\\begin{matrix}\\phantom{.}\\\\\\phantom{.}\\\\\\phantom{.}\\end{matrix}\\right)\\)</td>\n</tr>\n<tr>\n<td>[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "0", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "0", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "sortAnswers": false}, {"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 style=\"text-align: center;\">\\(\\var{v1}+\\var{v2}=\\) [[0]].</p>", "gaps": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "v1+v2", "correctAnswerFractions": false, "numRows": "2", "numColumns": 1, "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}], "sortAnswers": false}, {"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>Enter \\(\\pi\\) as pi.</p>\n<table>\n<tbody>\n<tr>\n<td rowspan=\"2\">\\(\\var{mu1}\\begin{pmatrix}\\sqrt{\\var{n}}\\\\\\var{w1[1]}\\end{pmatrix}+\\var{mu2}\\begin{pmatrix}-\\frac{\\sqrt{\\var{n}}}{\\var{b}}\\\\\\var{w2[1]}\\end{pmatrix}= \\left( \\begin{matrix}\\phantom{.}\\\\\\phantom{.}\\\\\\phantom{.}\\end{matrix}\\right.\\)</td>\n<td>[[0]]</td>\n<td rowspan=\"2\">\\(\\left.\\begin{matrix}\\phantom{.}\\\\\\phantom{.}\\\\\\phantom{.}\\end{matrix}\\right)\\)</td>\n</tr>\n<tr>\n<td>[[1]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "0", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, 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