Basic Solutions and Complementary Slackness in Pairs of Dual Systems
Consider the simultaneous linear system Ax = b where A is of order (m x n) and ρ(A) = ρ[A, b] (the system is consistent). If m < n, then we have an underdetermined equation system which, given that it is consistent, possesses an infinite number of particular solutions. Furthermore, let ρ(A) = m so that Ax = b is consistent for every b and none of the linear equations is redundant i.e., expressible as a linear combination of one or more other equations in the system.
KeywordsFeasible Solution Homogeneous Solution Basic Solution Basis Matrix Positive Variable
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