Online Homework Assignments. In homework 4 the terms ``one-to-one'' and ``onto'' are used.
A linear transformation T:R^m->R^n is onto, if im(T)=R^n.
A linear transformation T:R^m->R^n is one to one,
if the equation T(x)=b has at most one solution, for every b in R^n.
It is easy to see that a linear transformation is one-to-one,
if and only if ker(T)=(0).