Question: Let A be an m n matrix. A necessary and sufficient condition for the system of linear equations AT y = c to have

Let A be an m × n matrix. A necessary and sufficient condition for the system of linear equations AT y = c to have a nonnegative solution y ∈ ℜm+ is that cTx ≤ 0 for every x ∈ ℜn satisfying Ax ≤ 0.

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