Question: Assume the system Ax 0 has a solution, while Ax > 0 has no solution. Then A can be decomposed into two consistent subsystems

Assume the system Ax ≩ 0 has a solution, while Ax > 0 has no solution. Then A can be decomposed into two consistent subsystems
Bx > 0 and Cx = 0
such that Cx ≩ 0 has no solution.

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