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#### a)

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\$\\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*} \$

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#### b)

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\$\\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*} \$

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More information on multiplying matrices can be found in this Mathcentre leaflet.

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$AB = \\begin{pmatrix} \\var{a11}&\\var{a12}\\\\ \\var{a21}&\\var{a22}\\\\ \\end{pmatrix}\\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix} =$ []

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$CB = \\begin{pmatrix} \\var{c11}&\\var{c12}\\\\ \\var{c21}&\\var{c22}\\\\ \\end{pmatrix} \\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix}=$ []

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Let
\$A=\\begin{pmatrix} \\var{a11}&\\var{a12}\\\\ \\var{a21}&\\var{a22}\\\\ \\end{pmatrix},\\;\\; B=\\begin{pmatrix} \\var{b11}&\\var{b12}\\\\ \\var{b21}&\\var{b22}\\\\ \\end{pmatrix},\\;\\; C=\\begin{pmatrix} \\var{c11}&\\var{c12}\\\\ \\var{c21}&\\var{c22}\\\\ \\end{pmatrix}\$
Calculate the following products of these matrices:

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10/07/2012:

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Display of matrices looks untidy when individual components include negative numbers.

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Is it worthwhile restricting all components of matrices to be non zero?

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Question appears to be working correctly.

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Multiplication of $2 \\times 2$ matrices.

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