Use the Matrix Capabilities of a Graphing Utility to Reduce

Multiple Choice

Use the matrix capabilities of a graphing utility to reduce the augmented matrix corresponding to the system of equations, and solve the system. $$\left\{ \begin{aligned}x + 2 y + 2 z + 4 w & = 20 \\3 x + 6 y + 5 z + 12 w & = 53 \\x + 3 y - 3 z + 2 w & = - 18 \\6 x - y - z + w & = - 30\end{aligned} \right.$$

A) (-4, 1, 7, -2)
B) (-4, -1, 7, 2)
C) (-4, 1, -7, 2)
D) (-4, -1, -7, -2)
E) (-4, 1, 7, 2)