ANSWER
[tex]\begin{equation*} \begin{bmatrix}{4} & {6} & {3} \\ {-5} & {-1} & 1 \\ {} & {} & {}\end{bmatrix} \end{equation*}[/tex]
EXPLANATION
We want to translate triangle ABC by 2 units right and 4 units down.
To do this, we have to add 2 to the x-coordinates and subtract 4 from the y-coordinates of the vertices of the triangle.
In other words, add 2 to each value in the first row and subtract 4 from each value in the second row.
That is:
[tex]\begin{gathered} \begin{bmatrix}{2+2} & {4+2} & {1+2} \\ {-1-4} & {3-4} & {5-4} \\ {} & {} & {}\end{bmatrix} \\ \\ \begin{bmatrix}{4} & {6} & {3} \\ {-5} & {-1} & 1 \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]
That is the answer.
