Compute the indicated product [ ccc 2 & 3 & 4 3 & 4 & 5 4 & 5 & 6… - Vidyadip

Question

Compute the indicated product $\left[\begin{array}{ccc} {2} & {3} & {4} \\ {3} & {4} & {5} \\ {4} & {5} & {6} \end{array}\right]\left[\begin{array}{rrr} {1} & {-3} & {5} \\ {0} & {2} & {4} \\ {3} & {0} & {5} \end{array}\right]$

✓

Answer

We have, $\left[\begin{array}{lll} {2} & {3} & {4} \\ {3} & {4} & {5} \\ {4} & {5} & {6} \end{array}\right]\left[\begin{array}{rrr} {1} & {-3} & {5} \\ {0} & {2} & {4} \\ {3} & {0} & {5} \end{array}\right]$
= $\left[\begin{array}{ccc} {2(1)+3(0)+4(3)} & {2(-3)+3(2)+4(0)} & {2(5)+3(4)+4(5)} \\ {3(1)+4(0)+5(3)} & {3(-3)+4(2)+5(0)} & {3(5)+4(4)+5(5)} \\ {4(1)+5(0)+6(3)} & {4(-3)+5(2)+6(0)} & {4(5)+5(4)+6(5)} \end{array}\right]$
= $\left[\begin{array}{ccc} {2+0+12} & {-6+6+0} & {10+12+20} \\ {3+0+15} & {-9+8+0} & {15+16+25} \\ {4+0+18} & {-12+10+0} & {20+20+30} \end{array}\right]$
= $\left[\begin{array}{ccc} {14} & {0} & {42} \\ {18} & {-1} & {56} \\ {22} & {-2} & {70} \end{array}\right]$

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