Compute the indicated product [ rr 1 & -2 2 & 3 ] [ lll 1 & 2 & 3… - Vidyadip

Question

Compute the indicated product $\left[\begin{array}{rr} {1} & {-2} \\ {2} & {3} \end{array}\right]\left[\begin{array}{lll} {1} & {2} & {3} \\ {2} & {3} & {1} \end{array}\right]$

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Answer

$\left[\begin{array}{cc} {1} & {-2} \\ {2} & {3} \end{array}\right]\left[\begin{array}{lll} {1} & {2} & {3} \\ {3} & {2} & {1} \end{array}\right]$
= $\left[\begin{array}{lll} {1(1)-2(2)} & {1(2)-2(3)} & {1(3)-2(1)} \\ {2(1)+3(2)} & {2(2)+3(3)} & {2(3)+3(1)} \end{array}\right]$
= $\left[\begin{array}{ccc} {1-4} & {2-6} & {3-2} \\ {2+6} & {4+9} & {6+3} \end{array}\right]$
= $\left[\begin{array}{ccc} {-3} & {-4} & {1} \\ {8} & {13} & {9} \end{array}\right]$

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