Suppose A : n x n(adsbygoogle = window.adsbygoogle || []).push({});

A is invertible iff the columns (and rows) of A are linearly independent

A is invertible

iff det |A| is non-zero

iff rank A is n

iff column rank is n

iff dim (column space is n)

iff the n columns of A are linearly independent

Well, this is a proof that I laid down. It was junked by my prof. She said I have to use linear transformations to prove it. Someone throw some light ?

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# Matrix invertibility question

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