Corollary 2

Tag 05SW, permanent. Cite it as [Bourbaki, Tag 05SW].

For a homogeneous linear system (22) of equations in n unknowns with coefficients in a field $K$ to admit non-trivial solutions consisting of elements of $K$ , it is necessary and sufficient that its rank be < n.

This will always be the case if the number of equations is finite and < n.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

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Cites

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