(a) The matrix A 2714 4 14 30 can be shown to be symmetric positive definite. Compute an LU factorization of A by hand (do not do any pivoting) and then find the Cholesky factorization using the method described on page 115 of the x. You must calculate the intermediate matrices D, , and D before arriving at the matrix G such that A GGT (b) Compute the Cholesky decomposition of A by hand using the algorithm shown on page 116. Show the intermediate matrix after every iteration of the outer loop "for k-1:n 1". Verify that you get the same result as in part (a)