Which variable cannot be zero in underdetermined system?

Question

Consider the underdetermined system $Ax=b$, where $A \in R^{m\times n}$ with $m<n$. If the Matrix $A$ has rank $m$, my question is which variable of $x_1,x_2,\dots,x_n$ cannot be zero? I mean if we apply rref operations for the augmented matrix can we determine which variable cannot be zero? any constraints for variables corresponding to the linearly independent columns in $A$?