Answer
X =$\begin{bmatrix}
2 & -5 & 5\\
-5 & 0 & -6\\
\end{bmatrix}$
Work Step by Step
4B = -2X - 2A
2X = -2A - 4B
X = $\frac{1}{2}$(-2A - 4B)
First multiply matrix A by the scalar multiple -2:
$\begin{bmatrix}
-2(-2) & 1(-2) & 3(-2)\\
-1(-2) & 0(-2) & 4(-2)\\
\end{bmatrix}$ = $\begin{bmatrix}
4 & -2 & -6\\
2 & 0 & -8\\
\end{bmatrix}$
Then multiply matrix B by the scalar multiple -4:
$\begin{bmatrix}
0(-4) & 2(-4) & -4(-4)\\
3(-4) & 0(-4) & 1(-4)\\
\end{bmatrix}$ = $\begin{bmatrix}
0 & -8 & 16\\
-12 & 0 & -4\\
\end{bmatrix}$
Then perform -2A + -4B to get matrix Y:
Y = $\begin{bmatrix}
4+0 & -2-8 & -6+16\\
2-12 & 0+0 & -8-4\\
\end{bmatrix}$ = $\begin{bmatrix}
4 & -10 & 10\\
-10 & 0 & -12\\
\end{bmatrix}$
Then multiply Y by the scalar $\frac{1}{2}$ to get X:
X = $\begin{bmatrix}
4(\frac{1}{2}) & -10(\frac{1}{2}) & 10(\frac{1}{2})\\
-10(\frac{1}{2}) & 0(\frac{1}{2}) & -12(\frac{1}{2})\\
\end{bmatrix}$ = $\begin{bmatrix}
2 & -5 & 5\\
-5 & 0 & -6\\
\end{bmatrix}$
