Hi, I need help with this:

Let P be a non-empty polytope.

I) Prove that P has vertices.

II)Let be the vectrices of P. Show that

for the first one I see why P has vertices, if P is bounded and then if , 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!