Use Gauss-Jordan Row Reduction to Solve the Given System of Equations

Use Gauss-Jordan row reduction to solve the given system of equations.
$\begin{aligned}x + y + 5 z & = 3 \\y + 2 z + w & = 1 \\x + 3 y + 7 z + 2 w & = 4 \\x + y + 5 z + w & = 1\end{aligned}$

A) $\left( - \frac { 3 } { 2 } , 2 , \frac { 1 } { 2 } , - 2 \right)$
B) $\left( - \frac { 3 } { 2 } , 4 , \frac { 1 } { 4 } , - 2 \right)$
C) $\left( - \frac { 3 } { 2 } , 1 , \frac { 1 } { 2 } , - 2 \right)$
D) $\left( - \frac { 3 } { 2 } , 2 , \frac { 1 } { 2 } , - 1 \right)$
E) $\left( - \frac { 3 } { 4 } , 2 , \frac { 1 } { 2 } , - 2 \right)$

Correct Answer:

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