Solve the system of equations using matrices \[ \left\{\begin{array}{rr} x+y-z= & -5 \\ 5 x-y+z= & 5 \\ -x+3 y-2 z= & 1 \end{array}\right. \]

Step 1 ：Represent the system of equations in matrix form as \(AX = B\), where \(A\) is the coefficient matrix, \(X\) is the column matrix of variables, and \(B\) is the column matrix of constants.

Step 2 ：Write the coefficient matrix \(A\) as \(\begin{bmatrix} 1 & 1 & -1 \\ 5 & -1 & 1 \\ -1 & 3 & -2 \end{bmatrix}\)

Step 3 ：Write the column matrix of constants \(B\) as \(\begin{bmatrix} -5 \\ 5 \\ 1 \end{bmatrix}\)

Step 4 ：Calculate the inverse of matrix \(A\), denoted as \(A^{-1}\), which is \(\begin{bmatrix} 0.16666667 & 0.16666667 & 0 \\ -1.5 & 0.5 & 1 \\ -2.33333333 & 0.66666667 & 1 \end{bmatrix}\)

Step 5 ：Find the solution by multiplying the inverse of matrix \(A\) by matrix \(B\), which gives the column matrix of variables \(X\)

Step 6 ：The solution to the system of equations is \(\boxed{x = 0, y = 11, z = 16}\)