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 subset of Rⁿ. Show that pos S = pos (conv S).