Question: Let A be an m n matrix and c be a nonzero vector in n. Then exactly one of the following systems has a

Let A be an m × n matrix and c be a nonzero vector in ℜn. Then exactly one of the following systems has a nonnegative solution:
Either I Ax ≤ 0 and cx > 0 for some x ∈ Rn+
or II ATy ≥ c for some y ∈ Rm+.
Still other variants can be derived by creative reformulations of the alternative systems.

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