Since we are going to repeatedly solve the system a⃗x = ⃗b in the next problem, it makes sense to use lu decomposition. use the lu command to compute the lu factorization with partial pivoting lu = pa of the matrix a that you found in problem 1 as follows, [l, u,p] = lu(a); save the matrices l, u, and p into the files a4.dat, a5.dat, and a6.dat, respectively. solve the system a⃗x = ⃗b for the same values of w8, w9, w10, w11 you used in problem 2 using lu factorization with partial pivoting. save the intermediate result ⃗y (obtained through forward substitution, preceding backward substitution for ⃗x) to the file a7.dat and the final answer to the file a8.dat.