Given $A = \left[ \begin{array} { c c }
- 9 & 8 \
- 6 & - 5 \
10 & - 16
\end{array} \right]$ and $B = \left[ \begin{array} { l l }
1 & 0 \
2 & 3 \
0 & 4
\end{array} \right]$

, solve $2 X - A = 3 B$ , for $X$

A) $X = \left[ \begin{array} { l l l }
- 3 & 4 & 0 \
5 & 2 & 2
\end{array} \right]$

B) $X = \left[ \begin{array} { l l }
5 & 4 \
0 & 1 \
2 & 2
\end{array} \right]$

C) $X = \left[ \begin{array} { l l }
5 & \frac { 1 } { 2 } \
0 & 2 \
5 & 2
\end{array} \right]$

D) $X = \left[ \begin{array} { c c }
- 3 & 4 \
0 & 2 \
5 & - 2
\end{array} \right]$

E) none

Question

Given $A = \left[ \begin{array} { c c } 
- 9 & 8 \
- 6 & - 5 \
10 & - 16
\end{array} \right]$ and $B = \left[ \begin{array} { l l } 
1 & 0 \
2 & 3 \
0 & 4
\end{array} \right]$

, solve $2 X - A = 3 B$ , for $X$

A) $X = \left[ \begin{array} { l l l } 
- 3 & 4 & 0 \
5 & 2 & 2
\end{array} \right]$

B) $X = \left[ \begin{array} { l l } 
5 & 4 \
0 & 1 \
2 & 2
\end{array} \right]$

C) $X = \left[ \begin{array} { l l } 
5 & \frac { 1 } { 2 } \
0 & 2 \
5 & 2
\end{array} \right]$

D) $X = \left[ \begin{array} { c c } 
- 3 & 4 \
0 & 2 \
5 & - 2
\end{array} \right]$

E) none

Quizplus · Accepted Answer

First, move the $A$ term to the other side by adding both sides by $A$, and then divide everything by $2$:
\begin{align*}
2X-A&=3B \
2X&=3B+A\
\Rightarrow X&=\frac{3B+A}{2}
\end{align*}
Now, we just need to add the matrices:
$$X=\frac{1}{2} \left[ \begin{array}{cc} 1-18 & 0+8 \ 4-12 & 9-10 \ 0+20 & 12-32 \end{array} \right] = \left[ \begin{array}{cc} -3 & 4 \ 0 & 2 \ 5 & -2 \end{array} \right]$$
Therefore, the answer is $\boxed{\text{(D)}}$.

Given A=[−98−6−510−16]A = \left[ \begin{array} { c c } - 9 & 8 \\- 6 & - 5 \\10 & - 16\end{array} \right]A=​−9−610​8−5−16​​

Given $A = \left[ \begin{array} { c c } - 9 & 8 \\- 6 & - 5 \\10 & - 16\end{array} \right]$