Use the Gauss-Jordan Method to Solve the System of Equations $\begin{array}{l}x-y+z=4 \\x+y+z=-2 \\x+y-z=-12\end{array}$

Multiple Choice

Use the Gauss-Jordan method to solve the system of equations.
- $\begin{array}{l}x-y+z=4 \\x+y+z=-2 \\x+y-z=-12\end{array}$

A) $(-4,5,-3)$
B) $(-4,-3,5)$
C) $(5,-4,-3)$
D) No solution