Part C please

Assuming that LU factorization of A exists, prove that (a) (LDU factorization.) A can be written in the form A = LDU., where D is diagonal and L and Uj are unit lower and upper triangular matrices, respectively. (b) (LDL' factorization.) If A is symmetric, then A = LDLT. (c) Using (b), prove that if A is symmetric and positive definite, then A = HH . where H is a lower triangular matrix with positive diagonal entries. (This is known as the Cholesky decomposition.)Ans : from . ) A= LLC AT = A A = LV L'D25 I's on day But A = LDU , To V I' has Is on dlay. Symmetry =, AT = ( LDJ, ) = UTD LT T = 7 L' = LOV, T= L Ie VI= LT V ' = V = DL= V But A = LOV, = LDLT IT O