Suppose we have a matrix $A$. Define $\phi_{A}:\mathbb{F}^{n}\to\mathbb{F}^{m}$.
Consider the linear system $Ax=b$.
My textbook states that the above system is consistent $\iff$ $b_{i}=0$ for $i>k$ where $k$ is the number of pivots in $A$ in RREF.
What is your intuition of this since I don't really understand why.