Ml aggarwal solutions
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# Question 8

\text { 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] \text { and } C=\left[\begin{array}{cc} 1 & -5 \\ -4 & 6 \end{array}\right], find AB - 5C.

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Given

\begin{array}{l} A=\left[\begin{array}{ll} 3 & 7 \\ 2 & 4 \end{array}\right], \quad 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] \\ A B=\left[\begin{array}{ll} 3 & 7 \\ 2 & 4 \end{array}\right]\left[\begin{array}{ll} 0 & 2 \\ 5 & 3 \end{array}\right] \end{array}

On simplification we get

=\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 \mathrm{C}=5\left[\begin{array}{cc} 1 & -5 \\ -4 & 6 \end{array}\right]=\left[\begin{array}{cc} 5 & -25 \\ -20 & 30 \end{array}\right]

\mathrm{AB}-5 \mathrm{C}=\left[\begin{array}{cc} 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]

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