Finding a matrix from a formula for each entry, which involves the row and column numbers of that entry. Randomized size of the matrices and formula.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "Find the \\(\\var{m}\\times \\var{n}\\) matrix \\(A=(a_{ij})_{\\var{m}\\times \\var{n}}\\) whose entries satisfy the stated condition:
", "advice": "The entry \\(a_{ij}\\) is the entry in row \\(i\\) and column \\(j\\). So when we know the row and column, we can work out the entry from the formula.
\n\\(a_{ij}=\\var{latex(term('i',d1)+latexoperation+term('j',d2))}\\), so \\(a_{11}=\\var{a11}=\\var{A1[0][0]}\\) and \\(a_{12}=\\var{a12}=\\var{A1[0][1]}\\) and so on.
\n\\[ A = \\var{generalA} =\\var{unresolvedA1}= \\var{A1}\\]
", "rulesets": {}, "extensions": [], "variables": {"A1": {"name": "A1", "group": "Ungrouped variables", "definition": "matrix(map(rawA1[k..k+n],k,list(vector(0..m-1)*n)))", "description": "matrix([2,3,4,5],[3,4,5,6],[4,5,6,7],[5,6,7,8])
", "templateType": "anything"}, "generalA": {"name": "generalA", "group": "Ungrouped variables", "definition": "latex('\\\\begin{pmatrix}'+ concatstrings(rawgeneralA) +'\\\\end{'+'pmatrix}')\n", "description": "latex('\\\\begin{pmatrix} a_{11}&a_{12} & a_{13} & a_{14}\\\\\\\\ a_{21} & a_{22} & a_{23} & a_{24} \\\\\\\\ a_{31} & a_{32} & a_{33} & a_{34} \\\\\\\\ a_{41} & a_{42} & a_{43} & a_{44}\\\\end{pmatrix}')
", "templateType": "anything"}, "unresolvedA1": {"name": "unresolvedA1", "group": "Ungrouped variables", "definition": "latex('\\\\begin{pmatrix}'+ concatstrings(rawunresolvedA1) +'\\\\end{'+'pmatrix}')\n", "description": "latex('\\\\begin{pmatrix} 1+1&1+2 &1+3 & 1+4\\\\\\\\ 2+1 & 2+2 & 2+3 & 2+4 \\\\\\\\ 3+1 & 3+2 & 3+3 & 3+4 \\\\\\\\ 4+1 & 4+2 & 4+3 & 4+4\\\\end{pmatrix}')
", "templateType": "anything"}, "rawA1": {"name": "rawA1", "group": "Ungrouped variables", "definition": "map(eval(simplify(expression(termnumber({k},d1)+ '{operation}'+ termnumber({l},d2)),\"all\")),[k,l],product(1..m,1..n))", "description": "", "templateType": "anything"}, "rawunresolvedA1": {"name": "rawunresolvedA1", "group": "Ungrouped variables", "definition": "map(termnumber({k},d1)+ '{latexoperation}'+ termnumber({l},d2)+symbols[k-1][l-1],[k,l],product(1..m,1..n))", "description": "", "templateType": "anything"}, "symbols": {"name": "symbols", "group": "Ungrouped variables", "definition": "repeat(repeat('&',n-1)+['\\\\\\\\'],m-1)+[repeat('&',n-1)+['']]", "description": "['&','&','&','\\\\\\\\']
", "templateType": "anything"}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "number of columns
", "templateType": "anything"}, "rawgeneralA": {"name": "rawgeneralA", "group": "Ungrouped variables", "definition": "map('a_{'+'{k}'+'{l}}'+symbols[k-1][l-1],[k,l],product(1..m,1..n))", "description": "", "templateType": "anything"}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "number of rows
", "templateType": "anything"}, "operation": {"name": "operation", "group": "Ungrouped variables", "definition": "random(['+','-','*','^'])", "description": "random(['+','-','*','^'])
", "templateType": "anything"}, "latexoperation": {"name": "latexoperation", "group": "Ungrouped variables", "definition": "if(operation='*',latex('\\\\cdot'),latex(operation))", "description": "", "templateType": "anything"}, "a11": {"name": "a11", "group": "Ungrouped variables", "definition": "latex(termnumber(1,d1)+latexoperation+termnumber(1,d2))", "description": "", "templateType": "anything"}, "a12": {"name": "a12", "group": "Ungrouped variables", "definition": "latex(termnumber(1,d1)+latexoperation+termnumber(2,d2))", "description": "", "templateType": "anything"}, "term1test": {"name": "term1test", "group": "Ungrouped variables", "definition": "term('k',d1)", "description": "", "templateType": "anything"}, "d1": {"name": "d1", "group": "Ungrouped variables", "definition": "random(0..2)", "description": "", "templateType": "anything"}, "d2": {"name": "d2", "group": "Ungrouped variables", "definition": "random(0..2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["m", "n", "rawA1", "A1", "rawgeneralA", "generalA", "symbols", "rawunresolvedA1", "unresolvedA1", "operation", "latexoperation", "a11", "a12", "term1test", "d1", "d2"], "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;"}, "term": {"parameters": [["k", "string"], ["d", "number"]], "type": "string", "language": "jme", "definition": "switch(d=0,'{'+'('+k+'-1)'+'}',d=1,'{'+k+'}',d=2,'{'+'('+k+'+1)'+'}',k)"}, "termnumber": {"parameters": [["k", "number"], ["d", "number"]], "type": "number", "language": "jme", "definition": "switch(d=0,k-1,d=1,k,d=2,k+1,k)"}}, "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": "\\(a_{ij}=\\var{latex(term('i',d1)+latexoperation+term('j',d2))}\\). Then \\(A= \\) [[0]]
", "gaps": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "A1", "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", "type": "question", "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/"}]}