1 0 042 0 Consider the matrix A--2 2 3 . whose LU factorization is-1/2 1 001 3 4 -20 0 3 13 Derive the factorization A = LDU, where L is unit lower triangular, D is a. diagonal, and U' is unit upper triangular (Hint: let D take the diagonal elements of U, then define U, so that D U' = U} diagonal, and U, is unit upper triangular( Hint: let R = D1/2). factorization) b. Derive the factorization A = LRRU', where L is unit lower triangular, R is Derive the factorization A - MMT, where M is lower triangular (Cholesky c. 1 0 042 0 Consider the matrix A--2 2 3 . whose LU factorization is-1/2 1 001 3 4 -20 0 3 13 Derive the factorization A = LDU, where L is unit lower triangular, D is a. diagonal, and U' is unit upper triangular (Hint: let D take the diagonal elements of U, then define U, so that D U' = U} diagonal, and U, is unit upper triangular( Hint: let R = D1/2). factorization) b. Derive the factorization A = LRRU', where L is unit lower triangular, R is Derive the factorization A - MMT, where M is lower triangular (Cholesky c