Answer
$X=
\begin{bmatrix}
4 & -8
\\
-1 & -1
\\
11 & 1
\end{bmatrix}$
Work Step by Step
Using the properties of matrix equality, the given equation, $
\begin{bmatrix}
1 & 2
\\
2 & 1
\\
-3 & 4
\end{bmatrix}
+ X=
\begin{bmatrix}
5 & -6
\\
1 & 0
\\
8 & 5
\end{bmatrix}
,$ is equivalent to
\begin{align*}
\begin{bmatrix}
1 & 2
\\
2 & 1
\\
-3 & 4
\end{bmatrix}
-\begin{bmatrix}
1 & 2
\\
2 & 1
\\
-3 & 4
\end{bmatrix}
+ X&=
\begin{bmatrix}
5 & -6
\\
1 & 0
\\
8 & 5
\end{bmatrix}
-\begin{bmatrix}
1 & 2
\\
2 & 1
\\
-3 & 4
\end{bmatrix}
\\\\
X&=
\begin{bmatrix}
5 & -6
\\
1 & 0
\\
8 & 5
\end{bmatrix}
-\begin{bmatrix}
1 & 2
\\
2 & 1
\\
-3 & 4
\end{bmatrix}
\\\\
X&=
\begin{bmatrix}
5-1 & -6-2
\\
1-2 & 0-1
\\
8-(-3) & 5-4
\end{bmatrix}
\\\\
X&=
\begin{bmatrix}
4 & -8
\\
-1 & -1
\\
11 & 1
\end{bmatrix}
.\end{align*}
Hence, $
X=
\begin{bmatrix}
4 & -8
\\
-1 & -1
\\
11 & 1
\end{bmatrix}
$.
