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

Use Gauss-Jordan row reduction to solve the given system of equations. $$\begin{aligned}x - y + z - u + v & = 0 \\y - z + u - v & = - 8 \\x - 2 v & = - 12 \\2 x - y + z - u - 3 v & = - 16 \\4 x - y + z - u - 7 v & = - 40\end{aligned}$$

A) $( - 6 , - 16 + z - u , z , u , 1 )$ , z, u arbitrary
B) $( - 9 , - 6 + z - u , z , u , - 8 )$ , z, u arbitrary
C) $( - 8 , - 6 + z - u , z , u , 2 )$ , z, u arbitrary
D) $( - 8 , - 9 + z - u , z , u , 1 )$ , z, u arbitrary
E) $( 2 , - 6 + z - u , z , u , - 8 )$ , z, u arbitrary

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