In general, suppose two linear systems with the same number of equations and the same number of variables, then the system' augmented matrices have the same size. If the augmented matrices are row equivalent then the systems are having the same solutions.
So now I wonder, is it possible that two linear systems of $m$ equations and $n$ unknowns, having the same solutions, but their augmented matrices are not row equivalent?
P.S. I am just a noob in linear algebra. Sorry if my question is silly.
