Compute the indicated products. [ cc 2 & 1 3 & 2 -1 & 1 ] [ ccc 1… - Vidyadip

Question

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

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Answer

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

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