Originally Posted by

**adkinsjr** I have a question on a basic theorem:

--------------------------------------------------------------------------------------------------------------------------------

If A is a square matrix that can be reduced to row-echelon form, then __without interchanging any rows __then A can be factored as A=LU where U is the row-echelon form of A.

--------------------------------------------------------------------------------------------------------------------------------

This seems pretty simple, but it's not entirely clear why interchanging rows is illegal. Any clarification would be appreciated.