Please do b, c, and d

4. [40%] Consider the following four steps: (a) Use a single-precision routine for Gaussian elimination to solve the system Ax = b defined below: X1 1 X2 21.0 67.0 88.0 73.0 76.0 63.0 7.0 20.0 0.0 85.0 56.0 54.0 19.3 43.0 30.2 29.4 = 141.0 109.0 218.0 93.7 X3 24 (b) Compute the residual r = b Ax using double-precision arithmetic, but storing the final result in a single-precision vector r. (Note that the solution routine may destroy the matrix A, so you may need to save a separate copy for computing the residual.) (c) Solve the linear system Az = r to obtain the "improved solution x + z. (Note that the matrix A need not be refactored.) (d) Repeat steps b) and c) until no further improvement is observed. 4. [40%] Consider the following four steps: (a) Use a single-precision routine for Gaussian elimination to solve the system Ax = b defined below: X1 1 X2 21.0 67.0 88.0 73.0 76.0 63.0 7.0 20.0 0.0 85.0 56.0 54.0 19.3 43.0 30.2 29.4 = 141.0 109.0 218.0 93.7 X3 24 (b) Compute the residual r = b Ax using double-precision arithmetic, but storing the final result in a single-precision vector r. (Note that the solution routine may destroy the matrix A, so you may need to save a separate copy for computing the residual.) (c) Solve the linear system Az = r to obtain the "improved solution x + z. (Note that the matrix A need not be refactored.) (d) Repeat steps b) and c) until no further improvement is observed