Answer
$
X=
\begin{bmatrix}
-3 & 4
\\
-5 & 11
\end{bmatrix}$
Work Step by Step
Using the properties of matrix equality, the given matrix equation $
\begin{bmatrix}
6 & 1
\\
4 & -2
\end{bmatrix} + X = \begin{bmatrix}
3 & 5
\\
-1 & 9
\end{bmatrix}
,$ is equivalent to
\begin{align*}
\begin{bmatrix}
6 & 1
\\
4 & -2
\end{bmatrix}
-
\begin{bmatrix}
6 & 1
\\
4 & -2
\end{bmatrix}
+
X &= \begin{bmatrix}
3 & 5
\\
-1 & 9
\end{bmatrix}
-
\begin{bmatrix}
6 & 1
\\
4 & -2
\end{bmatrix}
\\\\
X &= \begin{bmatrix}
3 & 5
\\
-1 & 9
\end{bmatrix}
-
\begin{bmatrix}
6 & 1
\\
4 & -2
\end{bmatrix}
\\\\&=
\begin{bmatrix}
3-6 & 5-1
\\
-1-4 & 9-(-2)
\end{bmatrix}
\\\\&=
\begin{bmatrix}
-3 & 4
\\
-5 & 11
\end{bmatrix}
.\end{align*}
Hence, $
X=
\begin{bmatrix}
-3 & 4
\\
-5 & 11
\end{bmatrix}
$.
