Consider the following nonsingular (3 x 3) matrix and (3 X 1) vector: 0 A = 1 b = 0 2 (a) Perform LU Factorization (without pivoting) to produce both L and U so that A = LU. (You need to include all intermediate steps to receive full credit.) (b) Use your factorization to solve the linear system Ax = b by the two-step algorithm that involves first solving a lower-triangular system with L, followed by solving an upper-triangular system with U