3. (12pts) Answer the following questions: (a) Show that if a square matrix A has decomposition A = LLT with L nonsingular, then A is symmetric positive definite. (b) Find (by hand) the Cholesky factor L in the decomposition A = LLT for the 1 1 1 matrix A1 55 Solve the linear system Ax = b where 1 5 14, b = (3, 11, 20).