5 6 7 8 04 3 2 A = 000 1 00-1 -2 (a) The matrix A can be decomposed using partial pivoting as PA=LU, where U is upper triangular, L is unit lower triangular, and P is a permutation matrix. Find the 4 x 4 matrices U, L, and P. (b) Given the right-hand-side vector b = (26,9,1,-3), find x that satisfies Ax = b. (Show your method: do not just guess.) Let B be any real, nonsingular n x n matrix, where n is even, and set A = B-BT. Show that A does not admit an LU decomposition (i.e., some pivoting must be applied, even if A is monsingular).