Enter the matrix A and the vector b in MATLAB:

A = [4 1 2 −3; −3 3 −1 4; −1 2 5 1; 5 4 3 −1] , b = [−16;20;−4;−10]

The exact solution to the system Ax = b is the vector x = (−1, 1, −2, 3)^T .

(a) Enter [L, U,P] = lu(A) to find the LU decomposition of the matrix P A (don’t forget that you will need P*b). Verify that P A = LU.

(b) Use the LU decomposition you found in part (a) to solve the system Ax = b. Call the computed solution x_lu.

(c) Enter the vector x and compare your solution x lu from part (b) with the exact solution x by computing norm(x_lu - x)