linear algebra basis theorem Watch

shawn_o1
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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?
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DFranklin
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Use contradiction.
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Mark13
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(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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