// Numbas version: exam_results_page_options {"name": "mathcentre: Matrix arithmetic", "type": "exam", "duration": 0, "metadata": {"notes": "", "description": "
Three questions on linear combinations and products of matrices.
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\n\\[ \\begin{eqnarray*} \\simplify[std]{{p}A+{q}B} &=&\\simplify[std]{{p}{a}+{q}{b}}\\\\ &=& \\begin{pmatrix} \\simplify[std]{{p}*{a[0][0]}+{q}*{b[0][0]}}& \\simplify[std]{{p}*{a[0][1]}+{q}*{b[0][1]}}\\\\ \\simplify[std]{{p}*{a[1][0]}+{q}*{b[1][0]}}&\\simplify[std]{{p}*{a[1][1]}+{q}*{b[1][1]}} \\end{pmatrix}\\\\ &=&\\simplify{{lcab}}\\\\ \\end{eqnarray*} \\]
\n\\[ \\begin{eqnarray*} \\simplify[std]{{p1}A+{q1}B+{r1}C} &=&\\simplify[std]{{p1}{a}+{q1}{b}+{r1}{c}}\\\\ &=& \\begin{pmatrix} \\simplify[std]{{p1}*{a[0][0]}+{q1}*{b[0][0]}+{r1}*{c[0][0]}}& \\simplify[std]{{p1}*{a[0][1]}+{q1}*{b[0][1]}+{r1}*{c[0][1]}}\\\\ \\simplify[std]{{p1}*{a[1][0]}+{q1}*{b[1][0]}+{r1}*{c[1][0]}}&\\simplify[std]{{p1}*{a[1][1]}+{q1}*{b[1][1]}+{r1}*{c[1][1]}} \\end{pmatrix}\\\\ &=&\\simplify{{lcabc}}\\\\ \\end{eqnarray*} \\]
\n", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noleadingminus"]}, "parts": [{"prompt": "
$\\mathrm{A}+\\mathrm{B} = \\simplify[std]{{a}+{b}} = $ [[0]]
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\\[A=\\simplify{{a}},\\;\\; B=\\simplify{{b}},\\;\\; C=\\simplify{{c}}\\]
Calculate the following $2 \\times 2$ matrices:
", "type": "question", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "matrix(repeat(repeat(random(-5..5 except 0),2),2))", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "q1": {"definition": "random(-6..6 except [0,1,-1,p1,q])", "templateType": "anything", "group": "Ungrouped variables", "name": "q1", "description": ""}, "c": {"definition": "matrix(repeat(repeat(random(-5..5 except [0,a[0][0],b[0][0]]),2),2))", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "matrix(repeat(repeat(random(-5..5 except [0,a[0][0]]),2),2))", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "r1": {"definition": "random(-6..6 except [0,1,-1,p1,q1])", "templateType": "anything", "group": "Ungrouped variables", "name": "r1", "description": ""}, "q": {"definition": "random(-6..6 except [0,1,-1,p])", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random(2..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "p1": {"definition": "random(2..6 except p)", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}, "apb": {"definition": "a+b", "templateType": "anything", "group": "Ungrouped variables", "name": "apb", "description": ""}, "lcab": {"definition": "p*a+q*b", "templateType": "anything", "group": "Ungrouped variables", "name": "lcab", "description": ""}, "lcabc": {"definition": "p1*a+q1*b+r1*c", "templateType": "anything", "group": "Ungrouped variables", "name": "lcabc", "description": ""}}, "metadata": {"notes": "\n \t\t
8/02/2013:
\n \t\t
Finished first draft.
Linear combinations of $2 \\times 2$ matrices. Three examples.
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\n\\[A = \\left(\\begin{array}{rrr} \\var{a11} & \\var{a12} & \\var{a13}\\\\ \\var{a21} & \\var{a22} & \\var{a23}\\\\ \\var{a31} & \\var{a32} & \\var{a33}\\\\ \\end{array}\\right),\\;\\;\\;\\; B= \\left(\\begin{array}{rrr} \\var{b11} & \\var{b12} & \\var{b13}\\\\ \\var{b21} & \\var{b22} & \\var{b23}\\\\ \\var{b31} & \\var{b32} & \\var{b33}\\\\ \\end{array}\\right),\\;\\;\\;\\; v= \\left(\\begin{array}{r} \\var{v1}\\\\ \\var{v2} \\\\ \\var{v3} \\end{array}\\right),\\;\\;\\;\\; w= \\left(\\begin{array}{r} \\var{w1}\\\\ \\var{w2} \\\\ \\var{w3} \\end{array}\\right)\\]
\nFind the following products:
\n$Av = $ [[0]]
\n$Bw = $ [[1]]
\n$BA = $ [[2]]
\n$AB = $ [[3]]
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\n\\[\\begin{eqnarray}&C=& \\var{mac},\\;\\;\\;\\; &D=& \\var{mad},\\;\\;\\; \\;&E= &\\var{mae}\\\\&F=& \\left(\\begin{array}{rr} \\var{w1} & \\var{a12}\\\\ \\var{w2} & \\var{b23} \\\\ \\var{w3} & \\var{w2} \\\\\\var{v1} & \\var{b12}\\\\ 0 & \\var{-w2} \\end{array}\\right),\\;\\;\\;\\;&G=&\\var{mag},\\;\\;\\;\\;&H=&\\var{mah} \\end{eqnarray}\\]
\nWhich of the following products of matrices can be calculated?
\n[[0]]
\nPlease note that for every correct answer you get 0.5 marks and for every incorrect answer 0.5 is taken away. The minimum mark you can get is 0.
", "marks": 0, "gaps": [{"maxAnswers": 0, "matrix": "v", "shuffleAnswers": false, "shuffleChoices": true, "minAnswers": 0, "answers": ["Can be calculated", "Cannot be calculated"], "choices": ["$CD$
", "$DC$
", "$EF$
", "$FE$
", "$BC$
", "$AE$
", "$GH$
", "$HE$
", "$AG$
", "$GB$
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\n\n ", "type": "question", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"ba21": {"definition": "b21*a11+b22*a21+b23*a31", "templateType": "anything", "group": "Ungrouped variables", "name": "ba21", "description": ""}, "a21": {"definition": "random(-1,0,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a21", "description": ""}, "a22": {"definition": "random(-4,-3,-2,-1,1,2,3,5)", "templateType": "anything", "group": "Ungrouped variables", "name": "a22", "description": ""}, "a23": {"definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a23", "description": ""}, "b23": {"definition": "random(1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b23", "description": ""}, "b22": {"definition": "random(-4,-3,-2,-1,1,2,3,4)", "templateType": "anything", "group": "Ungrouped variables", "name": "b22", "description": ""}, "b21": {"definition": "random(0..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b21", "description": ""}, "ba22": {"definition": "b21*a12+b22*a22+b23*a32", "templateType": "anything", "group": "Ungrouped variables", "name": "ba22", "description": ""}, "w3": {"definition": "random(-4..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "w3", "description": ""}, "w2": {"definition": "random(-4..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "w2", "description": ""}, "w1": {"definition": "random(4..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "w1", "description": ""}, "mah": {"definition": "matrix(repeat(repeat(random(-2..9),x),y))", "templateType": "anything", "group": "Ungrouped variables", "name": "mah", "description": ""}, "ba32": {"definition": "b31*a12+b32*a22+b33*a32", "templateType": "anything", "group": "Ungrouped variables", "name": "ba32", "description": ""}, "q1": {"definition": "b11*w1+b12*w2+b13*w3", "templateType": "anything", "group": "Ungrouped variables", "name": "q1", "description": ""}, "q3": {"definition": "b31*w1+b32*w2+b33*w3", "templateType": "anything", "group": "Ungrouped variables", "name": "q3", "description": ""}, "q2": {"definition": "b21*w1+b22*w2+b23*w3", "templateType": "anything", "group": "Ungrouped variables", "name": "q2", "description": ""}, "ab23": {"definition": "a21*b13+a22*b23+a23*b33", "templateType": "anything", "group": "Ungrouped variables", "name": "ab23", "description": ""}, "ab22": {"definition": "a21*b12+a22*b22+a23*b32", "templateType": "anything", "group": "Ungrouped variables", "name": "ab22", "description": ""}, "ab21": {"definition": "a21*b11+a22*b21+a23*b31", "templateType": "anything", "group": "Ungrouped variables", "name": "ab21", "description": ""}, "s3": {"definition": "if(s=5,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s3", "description": ""}, "s2": {"definition": "if(q=m,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s2", "description": ""}, "s1": {"definition": "if(n=p,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}, "ba31": {"definition": "b31*a11+b32*a21+b33*a31", "templateType": "anything", "group": "Ungrouped variables", "name": "ba31", "description": ""}, "s7": {"definition": "if(u=y,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s7", "description": ""}, "s6": {"definition": "if(r=3,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s6", "description": ""}, "s5": {"definition": "if(m=3,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s5", "description": ""}, "s4": {"definition": "if(r=2,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s4", "description": ""}, "b12": {"definition": "random(0,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b12", "description": ""}, "b13": {"definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b13", "description": ""}, "b11": {"definition": "random(0,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b11", "description": ""}, "c13": {"definition": "random(1..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "c13", "description": ""}, "c12": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "c12", "description": ""}, "c11": {"definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "c11", "description": ""}, "ab11": {"definition": "a11*b11+a12*b21+a13*b31", "templateType": "anything", "group": "Ungrouped variables", "name": "ab11", "description": ""}, "a33": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a33", "description": ""}, "a32": {"definition": "random(-4..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a32", "description": ""}, "a31": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "a31", "description": ""}, "a11": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a11", "description": ""}, "ba33": {"definition": "b31*a13+b32*a23+b33*a33", "templateType": "anything", "group": "Ungrouped variables", "name": "ba33", "description": ""}, "a13": {"definition": "random(1..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a13", "description": ""}, "a12": {"definition": "random(-1,1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a12", "description": ""}, "s10": {"definition": "if(u=3,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s10", "description": ""}, "s9": {"definition": "if(w=3,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s9", "description": ""}, "b32": {"definition": "random(-3..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "b32", "description": ""}, "b31": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "b31", "description": ""}, "v1": {"definition": "random(-3..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "v1", "description": ""}, "mac": {"definition": "matrix(repeat(repeat(random(-2..9),n),m))", "templateType": "anything", "group": "Ungrouped variables", "name": "mac", "description": ""}, "v3": {"definition": "random(-5..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "v3", "description": ""}, "mae": {"definition": "matrix(repeat(repeat(random(-2..9),s),r))", "templateType": "anything", "group": "Ungrouped variables", "name": "mae", "description": ""}, "mad": {"definition": "matrix(repeat(repeat(random(-2..9),q),p))", "templateType": "anything", "group": "Ungrouped variables", "name": "mad", "description": ""}, "mag": {"definition": "matrix(repeat(repeat(random(-2..9),u),w))", "templateType": "anything", "group": "Ungrouped variables", "name": "mag", "description": ""}, "ba11": {"definition": "b11*a11+b12*a21+b13*a31", "templateType": "anything", "group": "Ungrouped variables", "name": "ba11", "description": ""}, "ba12": {"definition": "b11*a12+b12*a22+b13*a32", "templateType": "anything", "group": "Ungrouped variables", "name": "ba12", "description": ""}, "ba13": {"definition": "b11*a13+b12*a23+b13*a33", "templateType": "anything", "group": "Ungrouped variables", "name": "ba13", "description": ""}, "b33": {"definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b33", "description": ""}, "p2": {"definition": "a21*v1+a22*v2+a23*v3", "templateType": "anything", "group": "Ungrouped variables", "name": "p2", "description": ""}, "p3": {"definition": "a31*v1+a32*v2+a33*v3", "templateType": "anything", "group": "Ungrouped variables", "name": "p3", "description": ""}, "ba23": {"definition": "b21*a13+b22*a23+b23*a33", "templateType": "anything", "group": "Ungrouped variables", "name": "ba23", "description": ""}, "p1": {"definition": "a11*v1+a12*v2+a13*v3", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}, "s8": {"definition": "if(x=r,0.5,-0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "s8", "description": ""}, "ab31": {"definition": "a31*b11+a32*b21+a33*b31", "templateType": "anything", "group": "Ungrouped variables", "name": "ab31", "description": ""}, "ab32": {"definition": "a31*b12+a32*b22+a33*b32", "templateType": "anything", "group": "Ungrouped variables", "name": "ab32", "description": ""}, "ab33": {"definition": "a31*b13+a32*b23+a33*b33", "templateType": "anything", "group": "Ungrouped variables", "name": "ab33", "description": ""}, "ab12": {"definition": "a11*b12+a12*b22+a13*b32", "templateType": "anything", "group": "Ungrouped variables", "name": "ab12", "description": ""}, "m": {"definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "v2": {"definition": "random(1..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "v2", "description": ""}, "n": {"definition": "random(3..6 except m)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "m+random(0,z)", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "n+random(0,z)", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "random(4..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": {"definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "w": {"definition": "random(3..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "v": {"definition": "[[s1,-s1],[s2,-s2],[s3,-s3],[s4,-s4],[s5,-s5],[s6,-s6],[s7,-s7],[s8,-s8],[s9,-s9],[s10,-s10]]", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "y": {"definition": "u+random(0,z)", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "u+random(0,z)", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "z": {"definition": "random(-2,-1,1,2)", "templateType": "anything", "group": "Ungrouped variables", "name": "z", "description": ""}, "ab13": {"definition": "a11*b13+a12*b23+a13*b33", "templateType": "anything", "group": "Ungrouped variables", "name": "ab13", "description": ""}}, "metadata": {"notes": "\n \t\t \t\t \t\t
5/07/2012:
\n \t\t \t\t \t\tAdded tags.
\n \t\t \t\t \t\tQuestion appears to be working correctly.
\n \t\t \t\t \t\t\n \t\t \t\t \n \t\t \n \t\t", "description": "
Exercises in multiplying matrices.
", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Matrix Multiplication 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}, {"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "functions": {}, "ungrouped_variables": ["ba21", "a21", "a22", "ba22", "cb21", "b22", "b21", "cb22", "ac22", "ac21", "ab22", "ab21", "b12", "b11", "c12", "c11", "c22", "a11", "cb11", "cb12", "a12", "c21", "ba11", "ba12", "ab12", "ab11", "ac12", "ac11"], "tags": ["matrices", "matrix", "matrix multiplication", "matrix product", "multiplication of matrices", "multiplying matrices", "product of matrices"], "preamble": {"css": "", "js": ""}, "advice": "\\[ \\begin{eqnarray*} AB &=& \\begin{pmatrix} \\var{a11}&\\var{a12}\\\\ \\var{a21}&\\var{a22}\\\\ \\end{pmatrix}\\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix}\\\\ &=& \\begin{pmatrix} \\simplify[]{{a11}{b11}+{a12}{b21}}&\\simplify[]{{a11}{b12}+{a12}{b22}}\\\\ \\simplify[]{{a21}{b11}+{a22}{b21}}&\\simplify[]{{a21}{b12}+{a22}{b22}}\\\\ \\end{pmatrix}\\\\ &=& \\begin{pmatrix} \\var{ab11}&\\var{ab12}\\\\ \\var{ab21}&\\var{ab22}\\\\ \\end{pmatrix} \\end{eqnarray*} \\]
\n\\[ \\begin{eqnarray*} BA &=& \\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix}\\begin{pmatrix} \\var{a11}&\\var{a12}\\\\ \\var{a21}&\\var{a22}\\\\ \\end{pmatrix}\\\\ &=& \\begin{pmatrix} \\simplify[]{{b11}{a11}+{b12}{a21}}&\\simplify[]{{b11}{a12}+{b12}{a22}}\\\\ \\simplify[]{{b21}{a11}+{b22}{a21}}&\\simplify[]{{b21}{a12}+{b22}{a22}}\\\\ \\end{pmatrix}\\\\ &=& \\begin{pmatrix} \\var{ba11}&\\var{ba12}\\\\ \\var{ba21}&\\var{ba22}\\\\ \\end{pmatrix} \\end{eqnarray*} \\]
\n\\[ \\begin{eqnarray*} CB &=& \\begin{pmatrix} \\var{c11}&\\var{c12}\\\\ \\var{c21}&\\var{c22}\\\\ \\end{pmatrix}\\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix}\\\\ &=& \\begin{pmatrix} \\simplify[]{{c11}{b11}+{c12}{b21}}&\\simplify[]{{c11}{b12}+{c12}{b22}}\\\\ \\simplify[]{{c21}{b11}+{c22}{b21}}&\\simplify[]{{c21}{b12}+{a22}{b22}}\\\\ \\end{pmatrix}\\\\ &=& \\begin{pmatrix} \\var{cb11}&\\var{cb12}\\\\ \\var{cb21}&\\var{cb22}\\\\ \\end{pmatrix} \\end{eqnarray*} \\]
\n\\[ \\begin{eqnarray*} AC &=& \\begin{pmatrix} \\var{a11}&\\var{a12}\\\\ \\var{a21}&\\var{a22}\\\\ \\end{pmatrix}\\begin{pmatrix} \\var{c11}&\\var{c12}\\\\ \\var{c21}&\\var{c22}\\\\ \\end{pmatrix}\\\\ &=& \\begin{pmatrix} \\simplify[]{{a11}{c11}+{a12}{c21}}&\\simplify[]{{a11}{c12}+{a12}{c22}}\\\\ \\simplify[]{{a21}{c11}+{a22}{c21}}&\\simplify[]{{a21}{c12}+{a22}{c22}}\\\\ \\end{pmatrix}\\\\ &=& \\begin{pmatrix} \\var{ac11}&\\var{ac12}\\\\ \\var{ac21}&\\var{ac22}\\\\ \\end{pmatrix} \\end{eqnarray*} \\]
", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers"]}, "parts": [{"prompt": "$AB = \\begin{pmatrix} \\var{a11}&\\var{a12}\\\\ \\var{a21}&\\var{a22}\\\\ \\end{pmatrix}\\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix} = $ [[0]]
", "marks": 0, "gaps": [{"numColumns": "2", "type": "matrix", "allowFractions": false, "correctAnswerFractions": false, "markPerCell": false, "numRows": "2", "showCorrectAnswer": true, "correctAnswer": "matrix([\n [ab11,ab12],\n [ab21,ab22]\n])", "scripts": {}, "marks": 1, "tolerance": 0, "allowResize": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "$BA = \\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix}\\begin{pmatrix} \\var{a11}&\\var{a12}\\\\ \\var{a21}&\\var{a22}\\\\ \\end{pmatrix}=$ [[0]]
", "marks": 0, "gaps": [{"numColumns": "2", "type": "matrix", "allowFractions": false, "correctAnswerFractions": false, "markPerCell": false, "numRows": "2", "showCorrectAnswer": true, "correctAnswer": "matrix([\n [ba11,ba12],\n [ba21,ba22]\n])", "scripts": {}, "marks": 1, "tolerance": 0, "allowResize": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "$CB = \\begin{pmatrix} \\var{c11}&\\var{c12}\\\\ \\var{c21}&\\var{c22}\\\\ \\end{pmatrix} \\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix}=$ [[0]]
", "marks": 0, "gaps": [{"numColumns": "2", "type": "matrix", "allowFractions": false, "correctAnswerFractions": false, "markPerCell": false, "numRows": "2", "showCorrectAnswer": true, "correctAnswer": "matrix([\n [cb11,cb12],\n [cb21,cb22]\n])", "scripts": {}, "marks": 1, "tolerance": 0, "allowResize": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}, {"prompt": "$AC = \\begin{pmatrix} \\var{a11}&\\var{a12}\\\\ \\var{a21}&\\var{a22}\\\\ \\end{pmatrix}\\begin{pmatrix} \\var{c11}&\\var{c12}\\\\ \\var{c21}&\\var{c22}\\\\ \\end{pmatrix}=$ [[0]]
", "marks": 0, "gaps": [{"numColumns": "2", "type": "matrix", "allowFractions": false, "correctAnswerFractions": false, "markPerCell": false, "numRows": "2", "showCorrectAnswer": true, "correctAnswer": "matrix([\n [ac11,ac12],\n [ac21,ac22]\n])", "scripts": {}, "marks": 1, "tolerance": 0, "allowResize": false}], "showCorrectAnswer": true, "scripts": {}, "type": "gapfill"}], "statement": "\n \n \nDo the following matrix problems
Let
\\[A=\\begin{pmatrix} \\var{a11}&\\var{a12}\\\\ \\var{a21}&\\var{a22}\\\\ \\end{pmatrix},\\;\\;\n \n B=\\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix},\\;\\;\n \n C=\\begin{pmatrix} \\var{c11}&\\var{c12}\\\\ \\var{c21}&\\var{c22}\\\\ \\end{pmatrix}\\]
Calculate the following products of these matrices:
10/07/2012:
\n \t\t \t\tAdded tags.
\n \t\t \t\tDisplay of matrices looks untidy when individual components include negative numbers.
\n \t\t \t\tIs it worthwhile restricting all components of matrices to be non zero?
\n \t\t \t\tQuestion appears to be working correctly.
\n \t\t \n \t\t", "description": "Multiplication of $2 \\times 2$ matrices.
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