Answer
The matrix $3A+2D $ is, $3A+2D=\left[ \begin{array}{*{35}{l}}
2 & 3 & 8 \\
21 & 5 & 5 \\
\end{array} \right]$
Work Step by Step
Here we need to find $3A+2D $. Therefore consider, $\begin{align}
& 3A+2D=3\left[ \begin{array}{*{35}{l}}
2 & -1 & 2 \\
5 & 3 & -1 \\
\end{array} \right]+2\left[ \begin{array}{*{35}{l}}
-2 & 3 & 1 \\
3 & -2 & 4 \\
\end{array} \right] \\
& =\left[ \begin{array}{*{35}{l}}
3\times 2 & 3\times \left( -1 \right) & 3\times 2 \\
3\times 5 & 3\times 3 & 3\times \left( -1 \right) \\
\end{array} \right]+\left[ \begin{array}{*{35}{l}}
2\times \left( -2 \right) & 2\times 3 & 2\times 1 \\
2\times 3 & 2\times \left( -2 \right) & 2\times 4 \\
\end{array} \right] \\
& =\left[ \begin{array}{*{35}{l}}
6 & -3 & 6 \\
15 & 9 & -3 \\
\end{array} \right]+\left[ \begin{array}{*{35}{l}}
-4 & 6 & 2 \\
6 & -4 & 8 \\
\end{array} \right]
\end{align}$
Now we will add these matrices as shown below:
$\begin{align}
& \left[ \begin{array}{*{35}{l}}
6 & -3 & 6 \\
15 & 9 & -3 \\
\end{array} \right]+\left[ \begin{array}{*{35}{l}}
-4 & 6 & 2 \\
6 & -4 & 8 \\
\end{array} \right]=\left[ \begin{array}{*{35}{l}}
6-4 & -3+6 & 6+2 \\
15+6 & 9-4 & -3+8 \\
\end{array} \right] \\
& =\left[ \begin{array}{*{35}{l}}
2 & 3 & 8 \\
21 & 5 & 5 \\
\end{array} \right]
\end{align}$
Thus, $3A+2D=\left[ \begin{array}{*{35}{l}}
2 & 3 & 8 \\
21 & 5 & 5 \\
\end{array} \right]$
