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.

Given the right-hand-side vector b = (26,9,1, ?3) ^T , find x that satisfies Ax = b. (Show your method: do not just guess.)

Let B be any real, nonsingular n ? n matrix, where n is even, and set A = - B ^T . Show that A does not admit an LU decomposition (i.e., some pivoting must be applied, even if A is nonsingular).