Solve for X in the equation given. $9 A + 6 B = 3 X , A = \left[ \begin{array} { c c c } 6 & - 5 & 3 \ 8 & - 3 & - 7 \end{array} \right]$ and $B = \left[ \begin{array} { c c c } 3 & 5 & - 1 \ 1 & - 2 & 5 \end{array} \right]$
A) $\left[ \begin{array} { c c c } 72 & - 15 & 21 \ 78 & - 39 & - 33 \end{array} \right]$
B) $\left[ \begin{array} { c c c } 9 & 0 & 2 \ 9 & - 5 & - 2 \end{array} \right]$
C) $\left[ \begin{array} { c c c } 24 & - 5 & 7 \ 26 & - 13 & - 11 \end{array} \right]$
D) $\left[ \begin{array} { c c c } 12 & - 25 & 11 \ 22 & - 5 & - 31 \end{array} \right]$
E) not possible

Question

Quizplus · Accepted Answer

First, we multiply the matrices A and B to get 
$$AB=\begin{bmatrix} 3 & 7 & -13 \ -23 & -29 & 40\end{bmatrix}$$
Then, we use this result to find X: 
$$9A + 6B = 3X \implies X = 3(3A + 2B)$$
$$X = 3\begin{bmatrix} 18 & -15 & 9 \ 24 & -9 & -21\end{bmatrix} + 3\begin{bmatrix} 9 & 15 & -3 \ 3 & -6 & 15\end{bmatrix} =  \begin{bmatrix} 54 & -15 & 21 \ 78 & -39 & -33\end{bmatrix}$$
Therefore, the answer is choice C.

Solve for X in the Equation Given 9A+6B=3X,A=[6−538−3−7]9 A + 6 B = 3 X , A = \left[ \begin{array} { c c c } 6 & - 5 & 3 \\ 8 & - 3 & - 7 \end{array} \right]9A+6B=3X,A=[68​−5−3​3−7​]

Solve for X in the Equation Given $9 A + 6 B = 3 X , A = \left[ \begin{array} { c c c } 6 & - 5 & 3 \\ 8 & - 3 & - 7 \end{array} \right]$