Possible Row Reduced Echelon Forms

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This isn't homework.

I asked my professor for help on figuring out a way to know the possible combinations of reduced row echelon forms of nxn matrices, or mxn matrices.

He only could show me why it was really hard to find this out, not how to actually do it. His method was to use exhaustion on every row (i.e. consider every case on every row).

Are there simpler ways to figure this out?

Thanks for any help!


-F
 
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I'm not sure I understand your question, but if your nxn-matrix is invertible, then its
reduced-row-echelon is row-equivalent to the identity. Otherwise, its form will have
to see with the number of free variables vs. leading variables left after row reduction.
 

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