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Elementary Exercises in multiplying matrices. 

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Let

\n \n \n \n

\\[A = \\left(\\begin{array}{rrr} \\var{a11} & \\var{a12} & \\var{a13}\\\\ \\var{a21} & \\var{a22} & \\var{a23}\\\\ \\var{a31} & \\var{a32} & \\var{a33}\\\\\n \n \\end{array}\\right),\\;\\;\\;\\;\n \n B= \\left(\\begin{array}{rrr} \\var{b11} & \\var{b12} & \\var{b13}\\\\ \\var{b21} & \\var{b22} & \\var{b23}\\\\ \\var{b31} & \\var{b32} & \\var{b33}\\\\\n \n \\end{array}\\right),\\;\\;\\;\\;\n \n v= \\left(\\begin{array}{r} \\var{v1}\\\\ \\var{v2} \\\\ \\var{v3} \\end{array}\\right),\\;\\;\\;\\;\n \n w= \\left(\\begin{array}{r} \\var{w1}\\\\ \\var{w2} \\\\ \\var{w3} \\end{array}\\right)\\]

\n \n \n \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 \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 \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 \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]]
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$CD$

", "

$DC$

", "

$EF$

", "

$FE$

", "

$BC$

", "

$AE$

", "

$GH$

", "

$HE$

", "

$AG$

", "

$GB$

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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.

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"ba31": {"description": "", "definition": "b31*a11+b32*a21+b33*a31", "name": "ba31", "templateType": "anything", "group": "Ungrouped variables"}, "s1": {"description": "", "definition": "if(n=p,0.5,-0.5)", "name": "s1", "templateType": "anything", "group": "Ungrouped variables"}, "q2": {"description": "", "definition": "b21*w1+b22*w2+b23*w3", "name": "q2", "templateType": "anything", "group": "Ungrouped variables"}, "a32": {"description": "", "definition": "random(-4..4)", "name": "a32", "templateType": "anything", "group": "Ungrouped variables"}, "b22": {"description": "", "definition": "random(-4,-3,-2,-1,1,2,3,4)", "name": "b22", "templateType": "anything", "group": "Ungrouped variables"}, "b32": {"description": "", "definition": "random(-3..3)", "name": "b32", "templateType": "anything", "group": "Ungrouped variables"}, "ba21": {"description": "", "definition": "b21*a11+b22*a21+b23*a31", "name": "ba21", "templateType": "anything", "group": "Ungrouped variables"}, "ba11": {"description": "", "definition": "b11*a11+b12*a21+b13*a31", "name": "ba11", "templateType": "anything", "group": "Ungrouped variables"}, "b21": {"description": "", "definition": "random(0..2)", "name": "b21", "templateType": "anything", "group": "Ungrouped variables"}, "c11": {"description": "", "definition": "random(-2..2)", "name": "c11", "templateType": "anything", "group": "Ungrouped variables"}, "mad": {"description": "", "definition": "matrix(repeat(repeat(random(-2..9),q),p))", "name": "mad", "templateType": "anything", "group": "Ungrouped variables"}, "s9": {"description": "", "definition": "if(w=3,0.5,-0.5)", "name": "s9", "templateType": "anything", "group": "Ungrouped variables"}, "mae": {"description": "", "definition": "matrix(repeat(repeat(random(-2..9),s),r))", "name": "mae", "templateType": "anything", "group": "Ungrouped variables"}, "p3": {"description": "", "definition": "a31*v1+a32*v2+a33*v3", "name": "p3", "templateType": "anything", "group": "Ungrouped variables"}, "b11": {"description": "", "definition": "random(0,1)", "name": "b11", "templateType": "anything", "group": "Ungrouped variables"}, "u": {"description": "", "definition": "random(3..4)", "name": "u", "templateType": "anything", "group": "Ungrouped variables"}, "a23": {"description": "", "definition": "random(-2..2)", "name": "a23", "templateType": "anything", "group": "Ungrouped variables"}, "ba32": {"description": "", "definition": "b31*a12+b32*a22+b33*a32", "name": "ba32", "templateType": "anything", "group": "Ungrouped variables"}, "p2": {"description": "", "definition": "a21*v1+a22*v2+a23*v3", "name": "p2", "templateType": "anything", "group": "Ungrouped variables"}, "p1": {"description": "", "definition": "a11*v1+a12*v2+a13*v3", "name": "p1", "templateType": "anything", "group": "Ungrouped variables"}, "s3": {"description": "", "definition": "if(s=5,0.5,-0.5)", "name": "s3", "templateType": "anything", "group": "Ungrouped variables"}, "m": {"description": "", "definition": "random(3..4)", "name": "m", "templateType": "anything", "group": "Ungrouped variables"}}, "extensions": ["stats"], "type": "question", "preamble": {"js": "", "css": ""}, "advice": "", "statement": "

Answer the following questions on matrices.

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