Use the Gauss-Jordan Method to Solve the System of Equations $\begin{array} { l } x + 3 y - 2 z - w = 10 \\4 x + y + z + 2 w = 10 \\- 3 x - y - 3 z - 2 w = - 7 \\x - y - 3 z - 2 w = - 3\end{array}$

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.
$\begin{array} { l } x + 3 y - 2 z - w = 10 \\4 x + y + z + 2 w = 10 \\- 3 x - y - 3 z - 2 w = - 7 \\x - y - 3 z - 2 w = - 3\end{array}$

A) $\{ ( 0,5 , - 5,4 ) \}$
B) $\{ ( 10,10 , - 7 , - 3 ) \}$
C) $\{ ( 1 + w , 3 - 2 w , - 1 + 2 w , w ) \}$
D) $\{ ( 1,3 , - 1,2 ) \}$