Farkas' Lemma is a fundamental result in linear algebra and optimization that provides a criterion for the solvability of a system of linear inequalities. It states that either a given system of inequalities has a solution or there exists a non-negative linear combination of the inequalities that yields a contradiction, indicating that the inequalities are inconsistent. This concept is key to understanding feasibility in mathematical models and connects deeply with topics like unboundedness, extreme points, and path-following algorithms.
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