Answer
$X
=
\begin{bmatrix}
-5 & 5 & 4
\\
7& -10& 15
\end{bmatrix}$
Work Step by Step
Using the properties of matrix equality, the given matrix equation, $
X-\begin{bmatrix}
-3&2&-1
\\
6&-7&8
\end{bmatrix}
=
\begin{bmatrix}
-2&3&5
\\
1&-3&7
\end{bmatrix}
,$ is equivalent to
\begin{align*}
X-\begin{bmatrix}
-3&2&-1
\\
6&-7&8
\end{bmatrix}
+
\begin{bmatrix}
-3&2&-1
\\
6&-7&8
\end{bmatrix}
&=
\begin{bmatrix}
-2&3&5
\\
1&-3&7
\end{bmatrix}
+
\begin{bmatrix}
-3&2&-1
\\
6&-7&8
\end{bmatrix}
\\\\
X
&=
\begin{bmatrix}
-2+(-3)&3+2&5+(-1)
\\
1+6&-3+(-7)&7+8
\end{bmatrix}
\\\\
X
&=
\begin{bmatrix}
-2-3&3+2&5-1
\\
1+6&-3-7&7+8
\end{bmatrix}
\\\\
X
&=
\begin{bmatrix}
-5 & 5 & 4
\\
7& -10& 15
\end{bmatrix}
.\end{align*}
Hence, $
X
=
\begin{bmatrix}
-5 & 5 & 4
\\
7& -10& 15
\end{bmatrix}
.$
