Answer
The translated matrix is $B=\left[ \begin{matrix}
2 & 5 & 5 & 3 & 3 & 2 \\
-3 & -3 & -2 & -2 & 2 & 2 \\
\end{matrix} \right]$
The resulting graph is shown below:
Work Step by Step
Translate the L 2 units to the right and 3 units down by adding 2 to each $x\text{-coordinate}$
and subtracting 3 from each $y\text{-coordinate}$.
That is,
$\begin{align}
& B=\left[ \begin{matrix}
0 & 3 & 3 & 1 & 1 & 0 \\
0 & 0 & 1 & 1 & 5 & 5 \\
\end{matrix} \right]+\left[ \begin{matrix}
2 & 2 & 2 & 2 & 2 & 2 \\
-3 & -3 & -3 & -3 & -3 & -3 \\
\end{matrix} \right] \\
& =\left[ \begin{matrix}
2 & 5 & 5 & 3 & 3 & 2 \\
-3 & -3 & -2 & -2 & 2 & 2 \\
\end{matrix} \right]
\end{align}$
