Math Problem Statement
The following lemma (called Farkas’ Lemma) is a useful consequence of the separating hyperplane theorem. Lemma 1. Let A ∈ RM×N and b ∈ RM. Exactly one of the following is true: (a) there exists a vector x ∈ R N + such that Ax = b. (b) there exists λ ∈ RM such that AT λ ≤ 0, and λ T · b > 0.Prove the lemma (for arbitrary A).
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Algebra
Convex Sets
Separating Hyperplane Theorem
Formulas
-
Theorems
Farkas' Lemma
Suitable Grade Level
Advanced Undergraduate
Related Recommendation
Prove Farkas' Lemma: Fundamental Result in Linear Algebra and Optimization
Proof of Farkas' Lemma Using Convex Sets and Separation Theorem
Understanding Nonlinear Optimization with Bilinear Terms
Solving a Linear Programming Problem with Constraints
Fundamental Theorem of Duality in Linear Programming: Explanation and Proof