Solve for $X$ in the equation given.
$$3 X = 2 A - B , A = \left[ \begin{array} { c c }
- 6 & 2 \
8 & - 5
\end{array} \right] \text { and } B = \left[ \begin{array} { c c }
- 3 & 10 \
7 & - 1
\end{array} \right]$$
A) $\left[ \begin{array} { c c } - 3 & - 2 \ 3 & - 3 \end{array} \right]$
B) $\left[ \begin{array} { c c } - 9 & - 6 \ 9 & - 9 \end{array} \right]$
C) $\left[ \begin{array} { c c } - \frac { 1 } { 3 } & - \frac { 1 } { 2 } \ \frac { 1 } { 3 } & - \frac { 1 } { 3 } \end{array} \right]$
D) $\left[ \begin{array} { c c } - 3 & 2 \ - 3 & - 3 \end{array} \right]$
E) $\left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right]$

Question

Solve for $X$ in the equation given.
$$3 X = 2 A - B , A = \left[ \begin{array} { c c } 
- 6 & 2 \
8 & - 5
\end{array} \right] \text { and } B = \left[ \begin{array} { c c } 
- 3 & 10 \
7 & - 1
\end{array} \right]$$
A) $\left[ \begin{array} { c c } - 3 & - 2 \ 3 & - 3 \end{array} \right]$
B) $\left[ \begin{array} { c c } - 9 & - 6 \ 9 & - 9 \end{array} \right]$
C) $\left[ \begin{array} { c c } - \frac { 1 } { 3 } & - \frac { 1 } { 2 } \ \frac { 1 } { 3 } & - \frac { 1 } { 3 } \end{array} \right]$
D) $\left[ \begin{array} { c c } - 3 & 2 \ - 3 & - 3 \end{array} \right]$
E) $\left[ \begin{array} { l l } 1 & 0 \ 0 & 1 \end{array} \right]$

Quizplus · Accepted Answer

First, calculate $2A - B$. Matrix $A$ is $\left[ \begin{array} { c c } -6 & 2 \ 8 & -5 \end{array} \right]$ and matrix $B$ is $\left[ \begin{array} { c c } -3 & 10 \ 7 & -1 \end{array} \right]$. $$2A = 2 \times \left[ \begin{array} { c c } -6 & 2 \ 8 & -5 \end{array} \right] = \left[ \begin{array} { c c } -12 & 4 \ 16 & -10 \end{array} \right]$$$$2A - B = \left[ \begin{array} { c c } -12 & 4 \ 16 & -10 \end{array} \right] - \left[ \begin{array} { c c } -3 & 10 \ 7 & -1 \end{array} \right] = \left[ \begin{array} { c c } -9 & -6 \ 9 & -9 \end{array} \right]$$Since $3X = 2A - B$, we divide the resulting matrix by 3 to solve for $X$:$$X = \frac{1}{3} \times \left[ \begin{array} { c c } -9 & -6 \ 9 & -9 \end{array} \right] = \left[ \begin{array} { c c } -3 & -2 \ 3 & -3 \end{array} \right]$$

Solve For XXX In the Equation Given A) [−3−23−3]\left[ \begin{array} { c c } - 3 & - 2 \\ 3 & - 3 \end{array} \right][−33​−2−3​]

Solve For $X$ In the Equation Given A) $\left[ \begin{array} { c c } - 3 & - 2 \\ 3 & - 3 \end{array} \right]$