Let $Ax=b$ be a system of $r$ nonzero equations in $n$ unknowns.
Suppose that $rank(A)=rank(A|b)$ and that $(A|b)$ is in RRE.
We want to prove that.
The book says since $(A|b)$ is in reduced row echelon form, $(A|b)$ must have $r$ nonzero rows.
I can't follow the logic.
RRE form can have zero rows in the last position, then why it must have $r$ nonzero rows in here?