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Elementary Exercises in multiplying matrices. 

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true, "prompt": "\n \n \n

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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Answer the following questions on matrices.

\n

 

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"ab22", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "n": {"definition": "random(3..6 except m)", "name": "n", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "a11": {"definition": "random(1..4)", "name": "a11", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "b23": {"definition": "random(1,2)", "name": "b23", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "p": {"definition": "n+random(0,z)", "name": "p", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "m": {"definition": "random(3..4)", "name": "m", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "s4": {"definition": "if(r=2,0.5,-0.5)", "name": "s4", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "v2": {"definition": "random(1..4)", "name": "v2", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "mah": {"definition": "matrix(repeat(repeat(random(-2..9),x),y))", "name": "mah", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "v3": {"definition": "random(-5..5)", "name": "v3", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "s7": {"definition": "if(u=y,0.5,-0.5)", "name": "s7", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "z": {"definition": "random(-2,-1,1,2)", "name": "z", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "ba31": {"definition": "b31*a11+b32*a21+b33*a31", "name": "ba31", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "ab23": {"definition": "a21*b13+a22*b23+a23*b33", "name": "ab23", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "w2": {"definition": "random(-4..4)", "name": "w2", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "a13": {"definition": "random(1..2)", "name": "a13", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "q3": {"definition": "b31*w1+b32*w2+b33*w3", "name": "q3", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "b32": {"definition": "random(-3..3)", "name": "b32", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "a33": {"definition": "random(1..4)", "name": "a33", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "ab32": {"definition": "a31*b12+a32*b22+a33*b32", "name": "ab32", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "s9": {"definition": "if(w=3,0.5,-0.5)", "name": "s9", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "ba11": {"definition": "b11*a11+b12*a21+b13*a31", "name": "ba11", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "a21": {"definition": "random(-1,0,1)", "name": "a21", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "c12": {"definition": "random(1..3)", "name": "c12", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "ab31": {"definition": "a31*b11+a32*b21+a33*b31", "name": "ab31", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "mac": {"definition": "matrix(repeat(repeat(random(-2..9),n),m))", "name": "mac", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "mad": {"definition": "matrix(repeat(repeat(random(-2..9),q),p))", "name": "mad", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "s1": {"definition": "if(n=p,0.5,-0.5)", "name": "s1", "description": "", "group": "Ungrouped variables", "templateType": "anything"}, "ba21": {"definition": "b21*a11+b22*a21+b23*a31", "name": "ba21", "description": "", "group": "Ungrouped variables", 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