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Proof of the sufficiency of the determinant condition for the consistency of a system of n homogeneous linear equations In n variables

Published online by Cambridge University Press:  31 October 2008

John Dougall
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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 brevity we show the method by taking n = 3.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 12 , January 1913 , pp. 139
Copyright
Copyright © Edinburgh Mathematical Society 1913