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linear algebra basis theorem

If a1, ... , an are the columns of an invertible n x n matrix A, then the set of n vectors {a1, ... , an} forms a basis for Rn.


How do I prove this?
(edited 10 years ago)
Reply 1
Use contradiction.
Reply 2
Original post by shawn_o1
How do I prove this?


One way to do it is to show A invertible => A surjective => columns of A span R^n => columns of A form a basis of R^n.

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