Let A and b be the matrices A = 1 2 4 17
3 6 −12 3
2 3 −3 2
0 2 −2 6
and b = (17, 3, 3, 4) . (a) Explain why A does not have an LU
factorization. (b) Use partial pivoting and find the permutation
matrix P as well as the LU factors such that PA = LU. (c) Use the
information in P, L, and U to solve Ax = b