Answer
X = $\begin{bmatrix}
3 & -\frac{1}{2} & -\frac{13}{2}\\
3 & 0 & -\frac{11}{2}\\
\end{bmatrix}$
Work Step by Step
2X + 3A = B
2X = B - 3A
X = $\frac{1}{2}$(B - 3A)
First multiply matrix A by the scalar multiple 3:
$\begin{bmatrix}
-2(3) & 1(3) & 3(3)\\
-1(3) & 0(3) & 4(3)\\
\end{bmatrix}$ = $\begin{bmatrix}
-6 & 3 & 9\\
-3 & 0 & 12\\
\end{bmatrix}$
Then perform B - 3A to get matrix Y:
Y = $\begin{bmatrix}
0+6 & 2-3 & -4-9\\
3+3 & 0-0 & 1-12\\
\end{bmatrix}$ = $\begin{bmatrix}
6 & -1 & -13\\
6 & 0 & -11\\
\end{bmatrix}$
Then multiply matrix Y by the scalar $\frac{1}{2}$ to get matrix X:
X = $\begin{bmatrix}
6(\frac{1}{2}) & -1(\frac{1}{2}) & -13(\frac{1}{2})\\
6(\frac{1}{2}) & 0(\frac{1}{2}) & -11(\frac{1}{2})\\
\end{bmatrix}$ = $\begin{bmatrix}
3 & -\frac{1}{2} & -\frac{13}{2}\\
3 & 0 & -\frac{11}{2}\\
\end{bmatrix}$
