Solve the system. \[ \begin{array}{rr} -5 x-y= & -2 \\ y-2 z= & -1 \\ x-2 y+z= & 6 \end{array} \] Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution set is B. There are infinitely many solutions. C. There is no solution.

Step 1 ：Write the system of equations in matrix form. The matrix A is \[\begin{bmatrix} -5 & -1 & 0 \\ 0 & 1 & -2 \\ 1 & -2 & 1 \end{bmatrix}\] and the matrix b is \[\begin{bmatrix} -2 \\ -1 \\ 6 \end{bmatrix}\].

Step 2 ：Find the inverse of matrix A, if it exists.

Step 3 ：Multiplying the inverse of matrix A with matrix b to get the solution.

Step 4 ：The solution is x = 1, y = -3, z = -1.

Step 5 ：Final Answer: There is one solution. The solution set is \(\boxed{x = 1, y = -3, z = -1}\).