Let $T$ be a linear transformation from $\mathbb R^3$ to $\mathbb R^3$. Determine whether or not $T$ is onto.
- Suppose $T(4,-2,-2)= u$, $T(0,2,2)= v$, $T(4,1,0) = u + v$. Is $T$ onto?
I really do not know how to show if (1) is onto. I tried to to set $u$, $v$, $w = u+v$ as column vectors and from there determine if the columns span. But I'm not so sure if that's correct.
Or if $T$ is a one-to-one function then is also onto?