Question 3: Farkas' lemma for systems Ax ≥b. Complete the statement and write a complete proof of the following theorem, which is a version of Farkas' lemma for systems of the form Ax ≥ b. Theorem. Let A be a matrix of dimensions m x n and let b be a vector in Rm. Then, exactly one of the following two alternatives holds: (1) There exists some x ER" such that Ax ≥ b. (2) There exists some vector p You cannot use Theorem 4.6 (Farkas' lemma) to derive this result. You should prove it directly, similarly to how we proved Theorem 4.6 in class.

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