Question: Let A be an m n matrix. Then exactly one of the following systems has a nonnegative solution: Either I Ax > 0, x

Let A be an m × n matrix. Then exactly one of the following systems has a nonnegative solution:
Either I Ax > 0, x > 0 for some x ∈ ℜn
or II ATy ≤ 0, y ≩ 0 for some y ∈ ℜm.

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