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