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Proof of the sufficiency of the determinant condition for the consistency of a system of <i>n</i> homogeneous linear equations In <i>n</i> variables
For n = 1, the theorem is that, if a = 0, the equation ax = 0 has a solution for which x is not zero. This is obviously true. And the case of n variables can easily be made to depend on that of n – 1 variables. For …