Solve the system. \[ \begin{aligned} x-y+z & =-1 \\ -2 x+y+z & =7 \\ 2 x+4 y-2 z & =-4 \end{aligned} \]

Step 1 ：Given the system of equations: \[\begin{aligned} x-y+z & =-1 \\ -2 x+y+z & =7 \\ 2 x+4 y-2 z & =-4 \end{aligned}\]

Step 2 ：We can represent this system of equations in matrix form as: \[A = \begin{bmatrix} 1 & -1 & 1 \\ -2 & 1 & 1 \\ 2 & 4 & -2 \end{bmatrix}, b = \begin{bmatrix} -1 \\ 7 \\ -4 \end{bmatrix}\]

Step 3 ：By solving the matrix equation \(Ax = b\), we find the solution \(x = \begin{bmatrix} -2 \\ 1 \\ 2 \end{bmatrix}\)

Step 4 ：Thus, the solution to the system of equations is \(x = -2\), \(y = 1\), and \(z = 2\)

Step 5 ：Final Answer: \(\boxed{x = -2, y = 1, z = 2}\)