Given the matrices A and B, solve for X.
-$$2 X = 2 A - B$$
$A = \left[ \begin{array} { r r } - 6 & - 4 \ 6 & 4 \end{array} \right]$ and $B = \left[ \begin{array} { r r } - 8 & - 18 \ 6 & 16 \end{array} \right]$

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

B) $\left[ \begin{array} { r r } - 4 & 10 \ 6 & - 8 \end{array} \right]$

C) $\left[ \begin{array} { r r } - \frac { 1 } { 2 } & \frac { 1 } { 5 } \ \frac { 1 } { 3 } & - \frac { 1 } { 4 } \end{array} \right]$

D) $\left[ \begin{array} { r r } - 2 & 5 \ 3 & - 4 \end{array} \right]$

Question

Given the matrices A and B, solve for X.
-$$2 X = 2 A - B$$
$A = \left[ \begin{array} { r r } - 6 & - 4 \ 6 & 4 \end{array} \right]$ and $B = \left[ \begin{array} { r r } - 8 & - 18 \ 6 & 16 \end{array} \right]$

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

B) $\left[ \begin{array} { r r } - 4 & 10 \ 6 & - 8 \end{array} \right]$

C) $\left[ \begin{array} { r r } - \frac { 1 } { 2 } & \frac { 1 } { 5 } \ \frac { 1 } { 3 } & - \frac { 1 } { 4 } \end{array} \right]$

D) $\left[ \begin{array} { r r } - 2 & 5 \ 3 & - 4 \end{array} \right]$

Quizplus · Accepted Answer

To solve for X, first calculate $2A - B$:  $2A = \left[ \begin{array} { r r } -12 & -8 \ 12 & 8 \end{array} \right]$  $2A - B = \left[ \begin{array} { r r } -12 & -8 \ 12 & 8 \end{array} \right] - \left[ \begin{array} { r r } -8 & -18 \ 6 & 16 \end{array} \right] = \left[ \begin{array} { r r } -4 & 10 \ 6 & -8 \end{array} \right]$  Then, divide by 2:  $X = \frac{1}{2} \left[ \begin{array} { r r } -4 & 10 \ 6 & -8 \end{array} \right] = \left[ \begin{array} { r r } -2 & 5 \ 3 & -4 \end{array} \right]$  Thus, the correct answer is D.

Given the Matrices a and B, Solve for X 2X=2A−B2 X = 2 A - B2X=2A−B

Given the Matrices a and B, Solve for X $2 X = 2 A - B$