Finding the correct answer here is important, but perhaps equally important is finding it using the method of matrix reduction, since those are the instructions.

The augmented matrix is

4 -2 -5 -51

4 -1 -2 -36

4 -2 4 -24

You'll have to forgive the poor formatting. This answer box doesn't have a proper math symbol editor.

Using elementary row operations, the reduced row echelon form of the augmented matrix is

1 0 0 -6

0 1 0 6

0 0 1 3

from which we conclude that the system has a unique solution (-6,6,3).