Deal with the following concepts: A point p is called a positive combination of the points v₁,........., v_k if p = c₁v₁ +..........+c_kv_k, with all c_i ≥ 0. The set of all positive combinations of points of a set S is called the positive hull of S and is denoted by pos S.

Let S be a nonempty convex subset of Rⁿ. Prove x∈ pos S if and only if x = s for some λ ≥ 0 and some x in S.