Lu commands and related commands to solve 31 in matlab

USING MATLAB Consult online help for the command lu, and related com- mands. 31. The code [L,U] = lu(A) computes an LU-factorization of A, where L is a product of a lower triangular and permutation matrices. Row reduction in MATLAB uses partial pivoting to minimize round-off error and so we expect that some row exchanges may occur. Consider the matrix A=126 (a) Use hand calculation to reduce A to an upper triangu lar matrix U using partial pivoting, taking note of the interchanges that need to be made during reduction. (b) Find a permutation matrix P that reorders the rows of A so that no interchanges need to be made during reduction. (c) Use hand calculation to find an LU-factorization PA = LU. (d) Show that P-1-PT and check that A = PLU. (e) Find the MATLAB LU-factorization A, and compare your results