Corollary 1
Tag 05SV, permanent. Cite it as [Bourbaki, Tag 05SV].
Algebra, chapter II, § 7. Vector spaces
A system of scalar linear equations in a vector space, consisting of a finite number of equations whose left hand sides are linearly independent forms, always admits solutions.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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