We will solve for X in the matrix equation first,
[tex]\begin{gathered} -\frac{1}{2}A+\frac{1}{3}X=B \\ \frac{1}{3}X=B+\frac{1}{2}A \\ X=\frac{B+\frac{1}{2}A}{\frac{1}{3}} \\ X=3\times(B+\frac{1}{2}A) \end{gathered}[/tex]
We calculate (1/2 A) first and add it to B.
Then, multiply that matrix by the scalar constant "3".
The process is shown below:
[tex]\begin{gathered} X=3\times(B+\frac{1}{2}A) \\ X=3\times(\begin{bmatrix}-10 & 7 \\ 7 & 12\end{bmatrix}+\frac{1}{2}\begin{bmatrix}10 & -4 \\ -12 & 4\end{bmatrix}) \\ X=3\times(\begin{bmatrix}-10 & 7 \\ 7 & 12\end{bmatrix}+\begin{bmatrix}5 & -2 \\ -6 & 2\end{bmatrix}) \\ X=3\times\begin{bmatrix}-10+5 & 7-2 \\ 7-6 & 12+2\end{bmatrix} \\ X=3\times\begin{bmatrix}-5 & 5 \\ 1 & 14\end{bmatrix} \\ X=\begin{bmatrix}-15 & 15 \\ 3 & 42\end{bmatrix} \end{gathered}[/tex]
