Farkas lemma

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This result gives an alternative system, of which there are many. Farakas' Lemma states that exactly one of the following is consistent,

LaTeX: Ax = b, \; x \ge 0   (exclusive or)   LaTeX: A^Ty \ge 0, \; b^Ty < 0.

An often used variant is

LaTeX: Ax \ge b   (exclusive or)   LaTeX: A^Ty = 0, \; y \ge 0, \; b^Ty < 0.

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