1. Given the following 3 x 3 linear system 3x - 2y + 5z = 2 4x - 7y - z = 19 5x - 6y + 4z 13 = (a) Solve the linear system by using Gaussian elimination. (b) Let A be the coefficient matrix of the linear system. Find the LU decomposition of the matrix A. (c) Let xo be the right-hand side vector of the above linear system. Solve the following linear systems Axk+1=Xk, k = 0, 1, 2,..., to obtain x3. (Hint: Use the LU decomposition of A to save operation cost.)