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?

For a linear transformation $T$ from $\mathbb{R}^n$ to $\mathbb{R}^n$, the following are equivalent:
(1) $T$ is one-one
(2) $T$ is onto
(3) If $T(v)=0$, then $v=0$  
Generally, for a linear transformation $T: \mathbb{R}^n \longrightarrow \mathbb{R}^m$, the following are equivalent:
(1) $T$ is onto
(2) There is some basis $\mathcal{B}$ of $\mathbb{R}^m$ such that the image of $T$ contains $\mathcal{B}$
