If an inhomogeneous system of linear equations has an associated homogeneous system that has only the trivial solution, then how can I show that the inhomogeneous system has exactly one solution?
2026-05-05 20:54:31.1778014471
Solution for associated homogeneous linear system
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If an associated homogeneous system has only the trivial solution, then the zerovector has only a trivial representation. Columnvectors are all linear independent.
But if so, every vector, different from zerovector has unique representation with these independent columns.
By solving your inhomogeneous system, you are just calculating coordinates for the RHS-vector with respect to the given columns.