Question: The matrix
![842_B!.png](https://secure.tutorsglobe.com/CMSImages/842_B!.png)
is not positive definite but is positive semidefinite. Find a factorization B = LDLT, where L is lower triangular with ones on the diagonal and D is a diagonal matrix with nonnegative diagonal elements. If such a factorization exists for every symmetric positive semidefinite matrix, explain why. If not, give a counterexample.