Is there a way to test whether a matrix of linear equalities is consistent with a matrix of linear inequalities?

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Armin Fügenschuh

If you mean by "matrix of equalities" and "matrix of inequalities" that both are linear, then you can use linear optimization (Dantzig's Simplex algorithm) to find an answer: Just take all constraints together. This gives a joint linear optimization problem. You're only interested in a feasible solution. If one exists, then the constraints are not "mutually exclusive". If no such solution exists, then there are exclusive.

Bradley Ridder

Yes Dr. Fugenschuh, only linear constraints here.

(I assume it is very difficult to tell a priori whether a set of nonlinear constraints conflict with each other.)

Thank you! :)