Thread: Polytope

Hi, I need help with this:
Let P be a non-empty polytope.
I) Prove that P has vertices.
II)Let $\displaystyle u_1, \dots u_l \in \mathbb{R}^n$ be the vectrices of P. Show that $\displaystyle P=conv(\{u_1, \dots u_l \}).$

for the first one I see why P has vertices, if P is bounded and $\displaystyle P=\{ x \colon Ax\leq b \}$ then if $\displaystyle x \in P$, x is also bounded so A must be full colon rank. But this is just an idea and I'm not even sure it's correct.

if you can just give me a hit for II) it would be great.

Thanks in advance!

Hey sunmalus.

For those who are not familiar with polytypes (like myself), what is the structure of a polytype (like the set structure)?