// Numbas version: exam_results_page_options
{"name": "copy of Matrix times vector", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "copy of Matrix times vector", "tags": ["linear map", "matrix multiplication", "matrix times vector", "matrix transformation"], "metadata": {"description": "<p>Calculate matrix times vector.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Calculate the following:</p>", "advice": "<p>To calculate matrix times vector, we calculate this row by row: the first entry of the resulting vector is \"row 1 of the matrix times the vector\". For example</p>\n<p>\\[\\begin{pmatrix} a_{11} &amp; a_{12} \\\\ a_{21} &amp; a_{22}\\end{pmatrix} \\begin{pmatrix}x_1\\\\x_2\\end{pmatrix}= \\begin{pmatrix} a_{11}x_1+a_{12}x_2 \\\\ a_{21}x_1+a_{22}x_2\\end{pmatrix}\\]</p>\n<p>&nbsp;\\(\\var{A}\\var{va}=\\var{unresolvedAva}=\\var{A*va}\\)</p>", "rulesets": {}, "extensions": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": "matrix(repeat(repeat(random(-3..3),n),m))", "description": "", "templateType": "anything"}, "va": {"name": "va", "group": "Ungrouped variables", "definition": "vector(repeat(random(-2..2),n))", "description": "", "templateType": "anything"}, "rawunresolvedAva": {"name": "rawunresolvedAva", "group": "Ungrouped variables", "definition": "map(if({A[k][l]<0,'({A[k][l]})','{A[k][l]}')+'\\\\cdot'+if(va[l]<0,'({va[l]})','{va[l]}')+symbols(m,n)[k][l],[k,l],product(0..m-1,0..n-1))", "description": "<p>collects the terms \\(a_{ij}\\cdot v_j\\) for the matrix times vector multiplication, with plus symbols or new line concatenated ready to put into latex code for the calulcation steps of the matrix.</p>\n<p>All the \"if\" things are to put brackets round negative numbers. not using simplify because i prefer \\(\\cdot\\) to \\(\\times\\).</p>\n<p>Without the need for brackets, it could just be&nbsp; map('{A[k][l]}\\\\cdot{va[l]}'+symbols(2,2)[k][l],[k,l],product(0..1,0..1))</p>\n<p>The \"symbols\" is a function giving the correct addition or new line symbols for the size of the matrix that is being used.</p>", "templateType": "anything"}, "unresolvedAva": {"name": "unresolvedAva", "group": "Ungrouped variables", "definition": "latex('\\\\begin{pmatrix}'+ concatstrings(rawunresolvedAva) +'\\\\end{'+'pmatrix}')", "description": "<p>for the solution, the calculation steps written out unresolved.</p>", "templateType": "anything"}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["A", "va", "rawunresolvedAva", "unresolvedAva", "m", "n"], "variable_groups": [], "functions": {"concatstrings": {"parameters": [["input", "list"]], "type": "string", "language": "javascript", "definition": "var output = '';\nvar i;\nfor (i = 0; i < input.length; i++) {\n  output += input[i];\n} \nreturn output;"}, "symbols": {"parameters": [["m", "number"], ["n", "number"]], "type": "list", "language": "jme", "definition": "repeat(repeat('+',n-1)+['\\\\\\\\'],m-1)+[repeat('+',n-1)+['']]"}}, "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>\\(\\var{A}\\var{va}= \\) [[0]]</p>", "gaps": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "A*va", "correctAnswerFractions": false, "numRows": 1, "numColumns": 1, "allowResize": true, "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": "Julia Goedecke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5121/"}]}]}], "contributors": [{"name": "Julia Goedecke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5121/"}]}