(a)The reference they were referring is : "Find a lower triangular matrix L, and a diagonal matrix D such that ". I don't see how this is relevant though.

Here's what I've done so far

From this, critical points are

Since

The Hessian matrix will be

So what else do I need to do here to solve this? (I can't find any similar examples from my textbook)

Also, can anyone show me how to prove part(b). I don't understand it...