= Solution
Let $p$ be a <vertex of a linear polyhedron> and choose $n$ independent <active constraints>, written $Bp=d$, with $B$ invertible. Suppose $p=\lambda u+(1-\lambda)v$, where $u,v\in P$ and $0<\lambda<1$. Each selected inequality has $B_iu\leq d_i$ and $B_iv\leq d_i$, while
$$
d_i=B_ip=\lambda B_iu+(1-\lambda)B_iv.
$$
Since both weights are positive, equality in this weighted upper bound forces $B_iu=B_iv=d_i$ for every selected row. Hence $Bu=Bv=d$, and invertibility gives $u=v=p$. Therefore \b[every <vertex of a linear polyhedron> is an <extreme point>].
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