Compute the indicated products. [ rrr 3 & -1 & 3 -1 & 0 & 2 ] [ r… - Vidyadip

Question

Compute the indicated products.$\left[\begin{array}{rrr} {3} & {-1} & {3} \\ {-1} & {0} & {2} \end{array}\right]\left[\begin{array}{rr} {2} & {-3} \\ {1} & {0} \\ {3} & {1} \end{array}\right]$

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Answer

$\left[\begin{array}{ccc} {3} & {-1} & {3} \\ {-1} & {0} & {2} \end{array}\right]\left[\begin{array}{cc} {2} & {-3} \\ {1} & {0} \\ {3} & {1} \end{array}\right]$
= $\left[\begin{array}{cc} {3(2)-1(1)+3(3)} & {3(-3)-1(0)+3(1)} \\ {-1(2)+0(1)+2(3)} & {-1(-3)+0(0)+2(1)} \end{array}\right]$
= $\left[\begin{array}{cc} {6-1+9} & {-9-0+3} \\ {-2+0+6} & {3+0+2} \end{array}\right]$
= $\left[\begin{array}{cc} {14} & {-6} \\ {4} & {5} \end{array}\right]$

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