need help to prove the following: (already prove that both can't holds, but I need to show that if (a) doesn't hold then (b) hold)
Let A ∈ Mm×d(R). Prove that exactly one the following holds:
(a) There exists x ∈ $R^d$ such that Ax ≤ 0 and x > 0.
(b) There exists y ∈ $R^m$, satisfying y ≥ 0 and $y^T$A ≩ 0.