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5/07/2012:

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Question appears to be working correctly.

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\n \t\t \n \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "

Elementary Exercises in multiplying matrices.

"}, "parts": [{"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]]

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?

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[[0]]

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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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$HE$

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$AG$

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$GB$

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Answer the following questions on matrices.

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variables", "name": "w2", "definition": "random(-4..4)", "templateType": "anything", "description": ""}, "n": {"group": "Ungrouped variables", "name": "n", "definition": "random(3..6 except m)", "templateType": "anything", "description": ""}, "x": {"group": "Ungrouped variables", "name": "x", "definition": "u+random(0,z)", "templateType": "anything", "description": ""}, "ab22": {"group": "Ungrouped variables", "name": "ab22", "definition": "a21*b12+a22*b22+a23*b32", "templateType": "anything", "description": ""}, "ba13": {"group": "Ungrouped variables", "name": "ba13", "definition": "b11*a13+b12*a23+b13*a33", "templateType": "anything", "description": ""}, "w3": {"group": "Ungrouped variables", "name": "w3", "definition": "random(-4..4)", "templateType": "anything", "description": ""}, "a22": {"group": "Ungrouped variables", "name": "a22", "definition": "random(-4,-3,-2,-1,1,2,3,5)", "templateType": "anything", "description": ""}, "mae": {"group": "Ungrouped variables", "name": "mae", 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