5. (a) Prove that if all n leading principal minors of an n x n real matrix A are non-singular then A admits a Doolittle LU factorization. (b) Show that the following matrix A admits a Doolittle's LU factorization where 4 NO 2 4 2 0 A = 0 2 4 1 O and find its Doolittle's LU factorization. Hence or otherwise solve the linear system Ax = [0 0 0 1]T.(c) Prove or disprove that the Gouss-Sedel method when apply to solving Ax = [0 0 O 1]T in Question 5(b) converges to the solution for any initial guess x0. (15 Points)