If possible, find $5 A + 4 B$.
$$A = \left[ \begin{array} { r r r }
- 8 & 9 & 2 \
- 2 & 1 & - 4
\end{array} \right] , B = \left[ \begin{array} { c c c }
8 & 2 & 1 \
- 3 & 8 & 4
\end{array} \right]$$
A) $\left[ \begin{array} { c c c } - 72 & 37 & 6 \ 2 & - 27 & - 36 \end{array} \right]$
B) $\left[ \begin{array} { c c c } 0 & 11 & 3 \ - 5 & 9 & 0 \end{array} \right]$
C) $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \end{array} \right]$
D) $\left[ \begin{array} { c c c } - 8 & 53 & 14 \ - 22 & 37 & - 4 \end{array} \right]$
E) not possible

Question

If possible, find $5 A + 4 B$.
$$A = \left[ \begin{array} { r r r } 
- 8 & 9 & 2 \
- 2 & 1 & - 4
\end{array} \right] , B = \left[ \begin{array} { c c c } 
8 & 2 & 1 \
- 3 & 8 & 4
\end{array} \right]$$
A) $\left[ \begin{array} { c c c } - 72 & 37 & 6 \ 2 & - 27 & - 36 \end{array} \right]$
B) $\left[ \begin{array} { c c c } 0 & 11 & 3 \ - 5 & 9 & 0 \end{array} \right]$
C) $\left[ \begin{array} { l l l } 1 & 0 & 0 \ 0 & 1 & 0 \end{array} \right]$
D) $\left[ \begin{array} { c c c } - 8 & 53 & 14 \ - 22 & 37 & - 4 \end{array} \right]$
E) not possible

Quizplus · Accepted Answer

We can simply multiply each matrix by its scalars and add them together:
$$5A + 4B = 5\left[ \begin{array} { r r r } 
- 8 & 9 & 2 \
- 2 & 1 & - 4
\end{array} \right] + 4\left[ \begin{array} { c c c } 
8 & 2 & 1 \
- 3 & 8 & 4
\end{array} \right] = \left[ \begin{array} { c c c } - 40 & 45 & 10 \
- 10 & 5 & - 20 \end{array} \right] + \left[ \begin{array} { c c c } 
32 & 8 & 4 \
- 12 & 32 & 16
\end{array} \right] = \left[ \begin{array} { c c c } - 8 & 53 & 14 \
- 22 & 37 & - 4 \end{array} \right]$$
Therefore, the answer is choice D.

If Possible, Find 5A+4B5 A + 4 B5A+4B A) [−723762−27−36]\left[ \begin{array} { c c c } - 72 & 37 & 6 \\ 2 & - 27 & - 36 \end{array} \right][−722​37−27​6−36​]

If Possible, Find $5 A + 4 B$ A) $\left[ \begin{array} { c c c } - 72 & 37 & 6 \\ 2 & - 27 & - 36 \end{array} \right]$