Use Gauss-Jordan Elimination to Solve the Linear System and Determine $$\begin{aligned}x + y + z & = 7 \\x - y + 2 z & = 7 \\2 x + 3 z & = 14\end{aligned}$$

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.
- $$\begin{aligned}x + y + z & = 7 \\x - y + 2 z & = 7 \\2 x + 3 z & = 14\end{aligned}$$

A) $\left( - \frac { 3 z } { 2 } - 7,2 z , z \right)$
B) $\left( - \frac { 3 z } { 2 } + 7,2 z , z \right)$
C) $\left( - \frac { 3 z } { 2 } + 7 , \frac { z } { 2 } , z \right)$
D) $\left( - \frac { 3 z } { 2 } - 7 , \frac { z } { 2 } , z \right)$