2. (10 points) Given a real n-dimensional vector b and a matrix factorization A = LDL], where A is a n x n real symmetric positive definite matrix, D is a diagonal matrix, and L a lower tri- angular matrix with diagonal entries being ones. One uses the following algorithm to compute a vector x using b, D and L. for j = 1:n; yj = -bj - Ekiljkyki y, = -b, zj = yj/djji L end; for j = 1:n; i=n - j +1; di = zi - Ek=itl lkijk; end; In =- by- (ly, + ... Here bj and x; are the j-th elements of b and x respectively. dij and lij are the (i, j)-th entries of D and L respectively. (a) What is the relationship between a and b? You must show how you obtain your answer. First for loop Z = D ( - b - Ly ) Second for loop : n = 2 - Ly n = D ( - b - Ly ) - Ly. (b) What is the computational cost (leading order) of this algorithm? O(n ), note that Ike is O( n )