Use the Gauss-Jordan Method to Solve the System of Equations $$\begin{array} { l } x - y + 2 z + w = 5 \\y + z = 1 \\z - w = 4\end{array}$$

Multiple Choice

Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last
variable be the arbitrary variable.
- $$\begin{array} { l } x - y + 2 z + w = 5 \\y + z = 1 \\z - w = 4\end{array}$$

A) $\{ ( - 6 - 4 w , - 3 - w , 4 + w , w ) \}$
B) $\{ ( - 10 , - 4,5,1 ) \}$
C) $\varnothing$
D) $\{ ( - 6 , - 3,4 , \mathrm {~W} ) \}$