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

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.
$\begin{array} { l } x - y + 2 z + w = 1 \\y + z = 4 \\z - w = 1\end{array}$

A) $\{ ( 2,3,1 , w ) \}$
B) $\{ ( - 2,2,2,1 ) \}$
C) $\phi$
D) $\{ ( 2 - 4 w , 3 - w , 1 + w , w ) \}$