Question

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

• A. $$\left[\begin{array}{cc}40& 52\\ 30& -14\end{array}\right]$$
• B. $$\left[\begin{array}{cc}30& 52\\ 40& -14\end{array}\right]$$
• C. $$\left[\begin{array}{cc}40& 52\\ 30& 14\end{array}\right]$$
• D. $$\left[\begin{array}{cc}40& 52\\ 30& 24\end{array}\right]$$

Answer 1

The correct option is B

$$\left[\begin{array}{cc}30& 52\\ 40& -14\end{array}\right]$$

$AB-5C=\left[\begin{array}{cc}3& 7\\ 2& 4\end{array}\right]\left[\begin{array}{cc}0& 2\\ 5& 3\end{array}\right]-5\left[\begin{array}{cc}1& -5\\ -4& 6\end{array}\right]=\left[\begin{array}{cc}3\times 0+7\times 5& 3\times 2+7\times 3\\ 2\times 0+4\times 5& 2\times 2+4\times 3\end{array}\right]-\left[\begin{array}{cc}5& -25\\ -20& 30\end{array}\right]=\left[\begin{array}{cc}35& 27\\ 20& 16\end{array}\right]-\left[\begin{array}{cc}5& -25\\ -20& 30\end{array}\right]=\left[\begin{array}{cc}30& 52\\ 40& -14\end{array}\right]$