Answer
$4C+3D=\begin{bmatrix}
19 & 11
\\
-12 & 10
\end{bmatrix}$
Work Step by Step
Multiplying each element of $C=
\begin{bmatrix}
1 & 2
\\
-3 & 1
\end{bmatrix}
$ by $4,$ and then adding the result to $3$ times each element of $D=
\begin{bmatrix}
5 & 1
\\
0 & 2
\end{bmatrix}
,$ then
\begin{align*}
4C+3D&=
\begin{bmatrix}
1(4) & 2(4)
\\
-3(4) & 1(4)
\end{bmatrix}
+
\begin{bmatrix}
5(3) & 1(3)
\\
0(3) & 2(3)
\end{bmatrix}
\\\\&=
\begin{bmatrix}
4 & 8
\\
-12 & 4
\end{bmatrix}
+
\begin{bmatrix}
15 & 3
\\
0 & 6
\end{bmatrix}
\\\\&=
\begin{bmatrix}
4+15 & 8+3
\\
-12+0 & 4+6
\end{bmatrix}
\\\\&=
\begin{bmatrix}
19 & 11
\\
-12 & 10
\end{bmatrix}
.\end{align*}
Hence, $
4C+3D=\begin{bmatrix}
19 & 11
\\
-12 & 10
\end{bmatrix}
.$
