Set-systems with signed solutions Original Research Article

Qualitative properties of general collections of systems of m linear equations in n unknowns are studied. More precisely, a family Ax=B of systems of linear equations is determined by A=(A1,A2,…,An) where each Ai and B is a nonempty subset of image . The family consists of all systems image where the ith column of image belongs to Ai, and image belongs to B. These general collections include the purely qualitative systems (where each Ai and B is set of all vectors with a given sign pattern), cone-systems (where each Ai and B is a cone in image ), and interval systems (where each Ai and B is an interval of vectors). We give necessary and sufficient conditions on A and B for the sign patterns of the solutions to image to be independent of the choice of image and image