Use Gauss-Jordan Elimination to Solve the Linear System and Determine $$\begin{array} { r r } 5 x + 2 y + z & = - 11 \\2 x - 3 y - z & = 17 \\7 x - y & = 12\end{array}$$

Multiple Choice

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered
triple involving variable z.
- $$\begin{array} { r r } 5 x + 2 y + z & = - 11 \\2 x - 3 y - z & = 17 \\7 x - y & = 12\end{array}$$

A) $( - 2,0 , - 1 )$
B) $( 1 , - 5,0 )$
C) no solution
D) $( 0 , - 6,1 )$