Solve for $X$ in the equation given.
$$9 A + 6 B = 3 X , A = \left[ \begin{array} { c c c }
6 & - 5 & 3 \
8 & - 3 & - 7
\end{array} \right] \text { and } B = \left[ \begin{array} { c c c }
3 & 5 & - 1 \
1 & - 2 & 5
\end{array} \right]$$
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

Solve for $X$ in the equation given.
$$9 A + 6 B = 3 X , A = \left[ \begin{array} { c c c } 
6 & - 5 & 3 \
8 & - 3 & - 7
\end{array} \right] \text { and } B = \left[ \begin{array} { c c c } 
3 & 5 & - 1 \
1 & - 2 & 5
\end{array} \right]$$
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

Quizplus · Accepted Answer

We can first calculate the product of matrices A and B. Then we multiply the result with 3 and divide by 3, to obtain X.
$$ A \cdot B = \left[ \begin{array} { c c c }
(6 \cdot 3 + (-5) \cdot 1 + 3 \cdot (-1)) & (6 \cdot 5 + (-5) \cdot (-2) + 3 \cdot 5) & (6 \cdot (-1) + (-5) \cdot 5 + 3 \cdot (-1)) \ ( 8 \cdot 3 + (-3) \cdot 1 + (-7) \cdot (-1)) & (8 \cdot 5 + (-3) \cdot (-2) + (-7) \cdot 5) & (8 \cdot (-1) + (-3) \cdot 5 + (-7) \cdot (-1))
\end{array} \right] = \left[ \begin{array} { c c c }
24 & 26 & - 14 \ 8 & - 57 & - 34
\end{array} \right]$$
$$ 3 A \cdot B = \left[ \begin{array} { c c c }
72 & 78 & - 42 \ 24 & - 171 & - 102
\end{array} \right]$$
$$ X = \frac{3 A \cdot B}{3} = \left[ \begin{array} { c c c }
24 & - 5 & 7 \ 26 & - 13 & - 11
\end{array} \right]$$

Solve For XXX In the Equation Given A) [72−152178−39−33]\left[ \begin{array} { c c c } 72 & - 15 & 21 \\ 78 & - 39 & - 33 \end{array} \right][7278​−15−39​21−33​]

Solve For $X$ In the Equation Given A) $\left[ \begin{array} { c c c } 72 & - 15 & 21 \\ 78 & - 39 & - 33 \end{array} \right]$