What is the rule on the preservation of rank through an elementary operation? I know that rank can never go up, but is there any direct way to determine that it goes down (either than reducing the matrix down to row-echelon form)? Is there a good source that go into the proofs for properties of rank like this?(adsbygoogle = window.adsbygoogle || []).push({});

A side question is is it possible to have a linear dependency on rows as well as columns, or is the whole notion of such a dependency moot as both types are fungible?

Thanks

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# I Elementary operations & rank

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