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!