to $A$, and use $B$ to give all solutions of the system of linear equations. \[ A=\left[\begin{array}{rrrr} -1 & 1 & 1 & -5 \\ -1 & 3 & -9 & -19 \\ 7 & -2 & -32 & 0 \end{array}\right], \quad B=\left[\begin{array}{rrrr} 1 & 0 & -6 & -2 \\ 0 & 1 & -5 & -7 \\ 0 & 0 & 0 & 0 \end{array}\right] \]

Step 1 ：We are given two matrices A and B, where A represents the coefficients of the variables in the system of equations, and B represents the transformations applied to matrix A to simplify the system of equations.

Step 2 ：Matrix A is \[\begin{bmatrix} -1 & 1 & 1 & -5 \\ -1 & 3 & -9 & -19 \\ 7 & -2 & -32 & 0 \end{bmatrix}\] and matrix B is \[\begin{bmatrix} 1 & 0 & -6 & -2 \\ 0 & 1 & -5 & -7 \\ 0 & 0 & 0 & 0 \end{bmatrix}\].

Step 3 ：We can solve this system of equations using the Gaussian elimination method. This method involves performing row operations on the augmented matrix [A|B] to transform it into row echelon form or reduced row echelon form.

Step 4 ：After performing Gaussian elimination on the augmented matrix [A|B], we get \[\begin{bmatrix} 7 & -2 & -32 & 55 & 0 & 0 & 0 & 0 \\ 0 & 2 & -13 & 2 & 0 & 1 & -5 & -7 \\ 0 & 0 & -3 & -5 & 1 & 0 & -6 & -2 \end{bmatrix}\].

Step 5 ：The solutions to the system of equations can then be read off from the resulting matrix. The solutions are \(x = 7.85714286\), \(y = 1\), and \(z = 1.66666667\).

Step 6 ：Final Answer: The solutions to the system of equations are \(x = \boxed{7.85714286}\), \(y = \boxed{1}\), and \(z = \boxed{1.66666667}\).