Mathematics, Optimization, Data Science, Machine Learning, Duality.
matrix. Hence, the columns of the matrix are the 2-D vectors a₁ and a₂. Our vector x is only a length-2 vector, whose components are x₁ and x₂. Consequently, statement 1 of Farkas lemma means that the vector b is some weighted combination of a₁ and a₂, with all the weights —x₁ and x₂ — positive.