If A = [ ll 3 & 7 2 & 4 ], B = [ ll 0 & 2 5 & 3 ] and C = [ cc 1 & -5 -4 & 6 ] Find AB -5 C

& A = [ ll 3 & 7 2 & 4 ], B = [ ll 0 & 2 5 & 3 ] and C = [ cc 1 & -5 -4 & 6 ] & AB = [ ll 3 & 7 2 & 4 ] [ ll 0 & 2 5 & 3 ] & = [ ll 3 0+7 5 & 3 2+7 3 2 0+4 5 & 2 2+4 3 ] & = [ ll 0+35 & 6+21 0+20 & 4+12 ] & = [ ll 35 & 27 20 & 16 ] & 5 C =5 [ cc 1 & -5 -4 & 6 ] & = [ cc 5 & -25 -20 & 30 ] & AB -5 C = [ ll 35 & 27 20 & 16 ]- [ cc 5 & -25 -20 & 30 ] & = [ cc 30 & 52 40 & -14 ] .

If A = [ ll 3 & 7 2 & 4 ], B = [ ll 0 & 2 5 & 3 ] and C = [ cc 1 …

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Question

If $A =\left[\begin{array}{ll}3 & 7 \\ 2 & 4\end{array}\right], B =\left[\begin{array}{ll}0 & 2 \\ 5 & 3\end{array}\right]$ and $C =\left[\begin{array}{cc}1 & -5 \\ -4 & 6\end{array}\right]$ Find $AB -5 C$

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Answer

$\begin{aligned} & A =\left[\begin{array}{ll}3 & 7 \\ 2 & 4\end{array}\right], B =\left[\begin{array}{ll}0 & 2 \\ 5 & 3\end{array}\right] \text { and } C =\left[\begin{array}{cc}1 & -5 \\ -4 & 6\end{array}\right] \\ & AB =\left[\begin{array}{ll}3 & 7 \\ 2 & 4\end{array}\right]\left[\begin{array}{ll}0 & 2 \\ 5 & 3\end{array}\right] \\ & =\left[\begin{array}{ll}3 \times 0+7 \times 5 & 3 \times 2+7 \times 3 \\ 2 \times 0+4 \times 5 & 2 \times 2+4 \times 3\end{array}\right] \\ & =\left[\begin{array}{ll}0+35 & 6+21 \\ 0+20 & 4+12\end{array}\right] \\ & =\left[\begin{array}{ll}35 & 27 \\ 20 & 16\end{array}\right] \\ & 5 C =5\left[\begin{array}{cc}1 & -5 \\ -4 & 6\end{array}\right] \\ & =\left[\begin{array}{cc}5 & -25 \\ -20 & 30\end{array}\right] \\ & AB -5 C =\left[\begin{array}{ll}35 & 27 \\ 20 & 16\end{array}\right]-\left[\begin{array}{cc}5 & -25 \\ -20 & 30\end{array}\right] \\ & =\left[\begin{array}{cc}30 & 52 \\ 40 & -14\end{array}\right] .\end{aligned}$