Linear Algebra One to one and onto function I was just wondering how I can tell if a function is onto.
$\mathbf{R}^3\to\mathbf{R}^1$
Lets say the standard transformation matrix has vectors $\{1,0,0\}$, $\{0,1,0\}$, $\{0,0,0\}$.
I know that this transformation is not one to one since they vectors are not linearly independent. How can I see if the transformation is onto?

I generally try to use the Rank-Nullity theorem whenever I can.
The Rank Nullity Theorem. Let $f:V\rightarrow W$ be a linear map between finite-dimensional vector spaces $V$ and $W$. Then 
$$
\operatorname{rk}f+\operatorname{nul}f=\dim V
$$
where $\operatorname{rk}f:=\dim\operatorname{im}f$ and $\operatorname{nul}f:=\dim\ker f$.
So, to check if a linear map $f:\mathbb R^m\rightarrow\mathbb R^n$ is onto, we need only check that $\operatorname{nul}f=m-n$. 
