Prove that a square matrix is invertible if and only if its columns are linearly independent

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Payne

Mathematics

29 October, 20:12

Prove that a square matrix is invertible if and only if its columns are linearly independent

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Roman Sanford · Answer 1

Well, if the system is linearly dependent, then there's a vector that's "redundant". That is, it's a linear combination of the other vectors in the system. When you remove it, it is no longer a square matrix, and thus, not invertible.