Factor=.75 In this question, you are asked to develop an algorithm for LU-factoring a symmetric linear system. (a) You are given a linear system Ax = b, A symmetric and non-singular. Prove that Gauss elimination without pivoting (which is the name of the algorithm we studied in class) preserves the symmetry of A in the following sense: after elimination steps, the (m – j) * (m- ;) lower right portion of A; is still symmetric, i.e., the matrix Aj(j +1:m, j +1:m) is symmetric.