Answer
The matrix $-2A+4D $ is, $-2A+4D=\left[ \begin{array}{*{35}{l}}
-12 & 14 & 0 \\
2 & -14 & 18 \\
\end{array} \right]$.
Work Step by Step
Here we need to find $-2A+4D $. Therefore consider, $\begin{align}
& -2A+4D=-2\left[ \begin{array}{*{35}{l}}
2 & -1 & 2 \\
5 & 3 & -1 \\
\end{array} \right]+4\left[ \begin{array}{*{35}{l}}
-2 & 3 & 1 \\
3 & -2 & 4 \\
\end{array} \right] \\
& =\left[ \begin{array}{*{35}{l}}
-2\times 2 & -2\times -1 & -2\times 2 \\
-2\times 5 & -2\times 3 & -2\times -1 \\
\end{array} \right]+\left[ \begin{array}{*{35}{l}}
4\times -2 & 4\times 3 & 4\times 1 \\
4\times 3 & 4\times -2 & 4\times 4 \\
\end{array} \right] \\
& =\left[ \begin{array}{*{35}{l}}
-4 & 2 & -4 \\
-10 & -6 & 2 \\
\end{array} \right]+\left[ \begin{array}{*{35}{l}}
-8 & 12 & 4 \\
12 & -8 & 16 \\
\end{array} \right] \\
& =\left[ \begin{array}{*{35}{l}}
-12 & 14 & 0 \\
2 & -14 & 18 \\
\end{array} \right]
\end{align}$
Thus, $-2A+4D=\left[ \begin{array}{*{35}{l}}
-12 & 14 & 0 \\
2 & -14 & 18 \\
\end{array} \right]$.
