91Ó°ÊÓ

Prove that if the inequality \(A x \geq b\) has no nonnegative solution, then the inequalities \(A^{T} y \leq 0, b^{T} y>0\) have a nonnegative solution.

Prove that the closure of a convex set is convex.

Prove that if the system of inequalities \(\langle u, x\rangle>0\) for \(u \in U\) is consistent, then so is the system \(\langle u, x\rangle>0\) for \(u \in \operatorname{co}(U)\)