For what values of $s$ and $t$ is the matrix negative semidefinite? 
Let $$A =
\pmatrix{s&s&0\\
s&s&0\\
0&0&t}$$ where $s, t \in \mathbb R$ are parameters, and let $QA : R_
3 \to R$ be the corresponding quadratic form. Determine for which values of $s$ and $t$, $A$ and $QA$ are negative semidefinite and indefinite.

So far I calculated the product of X transposed AX and gave me that below:
(https://i.stack.imgur.com/9Xd9d.jpg)
I then said that this:
(https://i.stack.imgur.com/JmZUe.jpg)
Is that ok? If so how would I go about saying what values are indefinite.
Many thanks for you help.

If $\mathrm A$ is negative semidefinite then $-\mathrm A$ is positive semidefinite. Using  Sylvester's criterion, we obtain $$s, t \leq 0$$
