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I have been studying some linear algebra, and I recently came upon the method of finding determinants by row reduction (to row echelon form). But isn't it true than a matrix can have any row echelon form? If so, this would mean different determinants, right?

I am studying from "Elementary Linear Algebra With Applications" (ninth edition) by Howard Anton & Chris Rorres. In the first chapter it says "a row echelon form of a matrix is not unique", which only adds to my confusion.

Hopefully someone can shed some light on this issue with examples.

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# Determinants By Row Reduction/Row Echelon Form

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