// Numbas version: exam_results_page_options {"name": "Louise's copy of Ex 3 Matrix Multiplication 2", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": ["stats"], "parts": [{"customMarkingAlgorithm": "", "showCorrectAnswer": true, "marks": 0, "scripts": {}, "prompt": "

Let

\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)\$

\n

Find the following products:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 \$Av=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\$ [[0]] \$\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\$ [[1]] [[2]] \$Bw=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\$ [[3]] \$\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\$ [[4]] [[5]]
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 \$BA=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\$ [[6]] [[7]] [[8]] \$\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\$ [[9]] [[10]] [[11]] [[12]] [[13]] [[14]]
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 \$AB=\\left( \\begin{matrix} \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\$ [[15]] [[16]] [[17]] \$\\left) \\begin{matrix} \\phantom{.} \\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\phantom{.}\\\\ \\end{matrix} \\right.\$ [[18]] [[19]] [[20]] [[21]] [[22]] [[23]]

Consider the following matrices together with the matrices from the first part of the question.

\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}\$

\n

Which of the following products of matrices can be calculated?

\n

[[0]]

\n

Please 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.

", "type": "gapfill", "extendBaseMarkingAlgorithm": true, "unitTests": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"shuffleChoices": true, "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "matrix": "v", "extendBaseMarkingAlgorithm": true, "layout": {"expression": "", "type": "all"}, "answers": ["Can be calculated", "Cannot be calculated"], "minMarks": 0, "displayType": "radiogroup", "customMarkingAlgorithm": "", "warningType": "none", "variableReplacements": [], "choices": ["

$CD$

", "

$DC$

", "

$EF$

", "

$FE$

", "

$BC$

", "

$AE$

", "

$GH$

", "

$HE$

", "

$AG$

", "

$GB$

"], "marks": 0, "minAnswers": 0, "maxAnswers": 0, "type": "m_n_x", "unitTests": [], "showFeedbackIcon": true, "maxMarks": 0, "shuffleAnswers": false}], "variableReplacements": [], "sortAnswers": false}], "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["ba21", "a21", "a22", "a23", "b23", "b22", "b21", "ba22", "w3", "w2", "w1", "ba11", "a11", "ba13", "p1", "q1", "q", "q3", "q2", "ab23", "ab22", "ab21", "s3", "s2", "s1", "a12", "s7", "s6", "s5", "s4", "b12", "b13", "b11", "c13", "c12", "c11", "a33", "a32", "a31", "ba32", "ba33", "a13", "ba31", "s10", "s9", "b32", "b31", "v1", "v2", "v3", "mae", "mad", "mag", "mah", "ba12", "b33", "p2", "p3", "ba23", "ab11", "ab31", "ab32", "ab33", "ab12", "m", "s8", "n", "mac", "p", "s", "r", "u", "w", "v", "y", "x", "z", "ab13"], "name": "Louise's copy of Ex 3 Matrix Multiplication 2", "metadata": {"description": "

Elementary Exercises in multiplying matrices.

", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"b33": {"name": "b33", "description": "", "definition": "random(-2..2)", "group": "Ungrouped variables", "templateType": "anything"}, "ab22": {"name": "ab22", "description": "", "definition": "a21*b12+a22*b22+a23*b32", "group": "Ungrouped variables", "templateType": "anything"}, "s1": {"name": "s1", "description": "", "definition": "if(n=p,0.5,-0.5)", "group": "Ungrouped variables", "templateType": "anything"}, "ab33": {"name": "ab33", "description": "", "definition": "a31*b13+a32*b23+a33*b33", "group": "Ungrouped variables", "templateType": "anything"}, "ba11": {"name": "ba11", "description": "", "definition": "b11*a11+b12*a21+b13*a31", "group": "Ungrouped variables", "templateType": "anything"}, "ab11": {"name": "ab11", "description": "", "definition": "a11*b11+a12*b21+a13*b31", "group": "Ungrouped variables", "templateType": "anything"}, "a33": {"name": "a33", "description": "", "definition": "random(1..4)", "group": "Ungrouped variables", "templateType": "anything"}, "v": {"name": "v", "description": "", "definition": "[[s1,-s1],[s2,-s2],[s3,-s3],[s4,-s4],[s5,-s5],[s6,-s6],[s7,-s7],[s8,-s8],[s9,-s9],[s10,-s10]]", "group": "Ungrouped variables", "templateType": "anything"}, "s10": {"name": "s10", "description": "", "definition": "if(u=3,0.5,-0.5)", "group": "Ungrouped variables", "templateType": "anything"}, "ba23": {"name": "ba23", "description": "", "definition": "b21*a13+b22*a23+b23*a33", "group": "Ungrouped variables", "templateType": "anything"}, "a21": {"name": "a21", "description": "", "definition": "random(-1,0,1)", "group": "Ungrouped variables", "templateType": "anything"}, "q2": {"name": "q2", "description": "", "definition": "b21*w1+b22*w2+b23*w3", "group": "Ungrouped variables", "templateType": "anything"}, "ab13": {"name": "ab13", "description": "", "definition": "a11*b13+a12*b23+a13*b33", "group": "Ungrouped variables", "templateType": "anything"}, "a11": {"name": "a11", "description": "", "definition": "random(1..4)", "group": "Ungrouped variables", "templateType": "anything"}, "a23": {"name": "a23", "description": "", "definition": "random(-2..2)", "group": "Ungrouped variables", "templateType": "anything"}, "b32": {"name": "b32", "description": "", "definition": "random(-3..3)", "group": "Ungrouped variables", "templateType": "anything"}, "w": {"name": "w", "description": "", "definition": "random(3..5)", "group": "Ungrouped variables", "templateType": "anything"}, "w3": {"name": "w3", "description": "", "definition": "random(-4..4)", "group": "Ungrouped variables", "templateType": "anything"}, "c12": {"name": "c12", "description": "", "definition": "random(1..3)", "group": "Ungrouped variables", "templateType": "anything"}, "s4": {"name": "s4", "description": "", "definition": "if(r=2,0.5,-0.5)", "group": "Ungrouped variables", "templateType": "anything"}, "v1": {"name": "v1", "description": "", "definition": "random(-3..3)", "group": "Ungrouped variables", "templateType": "anything"}, "b21": {"name": "b21", "description": "", "definition": "random(0..2)", "group": "Ungrouped variables", "templateType": "anything"}, "s2": {"name": "s2", "description": "", "definition": "if(q=m,0.5,-0.5)", "group": "Ungrouped variables", "templateType": "anything"}, "z": {"name": "z", "description": "", "definition": "random(-2,-1,1,2)", "group": "Ungrouped variables", "templateType": "anything"}, "a31": {"name": "a31", "description": "", "definition": "random(1..3)", "group": "Ungrouped variables", "templateType": "anything"}, "b13": {"name": "b13", "description": "", "definition": "random(-2..2)", "group": "Ungrouped variables", "templateType": "anything"}, "ba33": {"name": "ba33", "description": "", "definition": "b31*a13+b32*a23+b33*a33", "group": "Ungrouped variables", "templateType": "anything"}, "a13": {"name": "a13", "description": "", "definition": "random(1..2)", "group": "Ungrouped variables", "templateType": "anything"}, "p3": {"name": "p3", "description": "", "definition": "a31*v1+a32*v2+a33*v3", "group": "Ungrouped variables", "templateType": "anything"}, "mad": {"name": "mad", "description": "", "definition": "matrix(repeat(repeat(random(-2..9),q),p))", "group": "Ungrouped variables", "templateType": "anything"}, "ba32": {"name": "ba32", "description": "", "definition": "b31*a12+b32*a22+b33*a32", "group": "Ungrouped variables", "templateType": "anything"}, "ba12": {"name": "ba12", "description": "", "definition": "b11*a12+b12*a22+b13*a32", "group": "Ungrouped variables", "templateType": "anything"}, "ba13": {"name": "ba13", "description": "", "definition": "b11*a13+b12*a23+b13*a33", "group": "Ungrouped variables", "templateType": "anything"}, "ab12": {"name": "ab12", "description": "", "definition": "a11*b12+a12*b22+a13*b32", "group": "Ungrouped variables", "templateType": "anything"}, "b22": {"name": "b22", "description": "", "definition": "random(-4,-3,-2,-1,1,2,3,4)", "group": "Ungrouped variables", "templateType": "anything"}, "b12": {"name": "b12", "description": "", "definition": "random(0,1)", "group": "Ungrouped variables", "templateType": "anything"}, "v3": {"name": "v3", "description": "", "definition": "random(-5..5)", "group": "Ungrouped variables", "templateType": "anything"}, "p": {"name": "p", "description": "", "definition": "n+random(0,z)", "group": "Ungrouped variables", "templateType": "anything"}, "b31": {"name": "b31", "description": "", "definition": "random(1..3)", "group": "Ungrouped variables", "templateType": "anything"}, "m": {"name": "m", "description": "", "definition": "random(3..4)", "group": "Ungrouped variables", "templateType": "anything"}, "mae": {"name": "mae", "description": "", "definition": "matrix(repeat(repeat(random(-2..9),s),r))", "group": "Ungrouped variables", "templateType": "anything"}, "s7": {"name": "s7", "description": "", "definition": "if(u=y,0.5,-0.5)", "group": "Ungrouped variables", "templateType": "anything"}, "b23": {"name": "b23", "description": "", "definition": "random(1,2)", "group": "Ungrouped variables", "templateType": "anything"}, "s3": {"name": "s3", "description": "", "definition": "if(s=5,0.5,-0.5)", "group": "Ungrouped variables", "templateType": "anything"}, "s5": {"name": "s5", "description": "", "definition": "if(m=3,0.5,-0.5)", "group": "Ungrouped variables", "templateType": "anything"}, "r": {"name": "r", "description": "", "definition": "random(1..3)", "group": "Ungrouped variables", "templateType": "anything"}, "q1": {"name": "q1", "description": "", "definition": "b11*w1+b12*w2+b13*w3", "group": "Ungrouped variables", "templateType": "anything"}, "c13": {"name": "c13", "description": "", "definition": "random(1..2)", "group": "Ungrouped variables", "templateType": "anything"}, "q": {"name": "q", "description": "", "definition": "m+random(0,z)", "group": "Ungrouped variables", "templateType": "anything"}, "ba21": {"name": "ba21", "description": "", "definition": "b21*a11+b22*a21+b23*a31", "group": "Ungrouped variables", "templateType": "anything"}, "a22": {"name": "a22", "description": "", "definition": "random(-4,-3,-2,-1,1,2,3,5)", "group": "Ungrouped variables", "templateType": "anything"}, "ab31": {"name": "ab31", "description": "", "definition": "a31*b11+a32*b21+a33*b31", "group": "Ungrouped variables", "templateType": "anything"}, "w2": {"name": "w2", "description": "", "definition": "random(-4..4)", "group": "Ungrouped variables", "templateType": "anything"}, "p2": {"name": "p2", "description": "", "definition": "a21*v1+a22*v2+a23*v3", "group": "Ungrouped variables", "templateType": "anything"}, "v2": {"name": "v2", "description": "", "definition": "random(1..4)", "group": "Ungrouped variables", "templateType": "anything"}, "ab32": {"name": "ab32", "description": "", "definition": "a31*b12+a32*b22+a33*b32", "group": "Ungrouped variables", "templateType": "anything"}, "s9": {"name": "s9", "description": "", "definition": "if(w=3,0.5,-0.5)", "group": "Ungrouped variables", "templateType": "anything"}, "a12": {"name": "a12", "description": "", "definition": "random(-1,1,2)", "group": "Ungrouped variables", "templateType": "anything"}, "s": {"name": "s", "description": "", "definition": "random(4..6)", "group": "Ungrouped variables", "templateType": "anything"}, "u": {"name": "u", "description": "", "definition": "random(3..4)", "group": "Ungrouped variables", "templateType": "anything"}, "w1": {"name": "w1", "description": "", "definition": "random(4..6)", "group": "Ungrouped variables", "templateType": "anything"}, "mah": {"name": "mah", "description": "", "definition": "matrix(repeat(repeat(random(-2..9),x),y))", "group": "Ungrouped variables", "templateType": "anything"}, "c11": {"name": "c11", "description": "", "definition": "random(-2..2)", "group": "Ungrouped variables", "templateType": "anything"}, "x": {"name": "x", "description": "", "definition": "u+random(0,z)", "group": "Ungrouped variables", "templateType": "anything"}, "ba22": {"name": "ba22", "description": "", "definition": "b21*a12+b22*a22+b23*a32", "group": "Ungrouped variables", "templateType": "anything"}, "s8": {"name": "s8", "description": "", "definition": "if(x=r,0.5,-0.5)", "group": "Ungrouped variables", "templateType": "anything"}, "p1": {"name": "p1", "description": "", "definition": "a11*v1+a12*v2+a13*v3", "group": "Ungrouped variables", "templateType": "anything"}, "a32": {"name": "a32", "description": "", "definition": "random(-4..4)", "group": "Ungrouped variables", "templateType": "anything"}, "n": {"name": "n", "description": "", "definition": "random(3..6 except m)", "group": "Ungrouped variables", "templateType": "anything"}, "mag": {"name": "mag", "description": "", "definition": "matrix(repeat(repeat(random(-2..9),u),w))", "group": "Ungrouped variables", "templateType": "anything"}, "mac": {"name": "mac", "description": "", "definition": "matrix(repeat(repeat(random(-2..9),n),m))", "group": "Ungrouped variables", "templateType": "anything"}, "b11": {"name": "b11", "description": "", "definition": "random(0,1)", "group": "Ungrouped variables", "templateType": "anything"}, "y": {"name": "y", "description": "", "definition": "u+random(0,z)", "group": "Ungrouped variables", "templateType": "anything"}, "s6": {"name": "s6", "description": "", "definition": "if(r=3,0.5,-0.5)", "group": "Ungrouped variables", "templateType": "anything"}, "ab23": {"name": "ab23", "description": "", "definition": "a21*b13+a22*b23+a23*b33", "group": "Ungrouped variables", "templateType": "anything"}, "q3": {"name": "q3", "description": "", "definition": "b31*w1+b32*w2+b33*w3", "group": "Ungrouped variables", "templateType": "anything"}, "ab21": {"name": "ab21", "description": "", "definition": "a21*b11+a22*b21+a23*b31", "group": "Ungrouped variables", "templateType": "anything"}, "ba31": {"name": "ba31", "description": "", "definition": "b31*a11+b32*a21+b33*a31", "group": "Ungrouped variables", "templateType": "anything"}}, "statement": "

Answer the following questions on matrices.

\n

", "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "functions": {}, "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "variable_groups": [], "advice": "", "type": "question", "contributors": [{"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}, {"name": "Louise Lynch", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2197/"}]}]}], "contributors": [{"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}, {"name": "Louise Lynch", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2197/"}]}