Computing image under coordinate map How do I compute the image?
Compute the image of (1,2,3,4) under the coordinate map
$$ \begin{bmatrix}t^3&t^3 + t^2&t^3+t^2+t&t^3+t^2+t+1\end{bmatrix}: \Bbb F^4\to P_3.$$

I assume they expect you to do 
\begin{align}
\begin{bmatrix}t^3&t^3 + t^2&t^3+t^2+t&t^3+t^2+t+1\end{bmatrix}\begin{bmatrix}1\\2\\3\\4\end{bmatrix}
&=t^3+2(t^3+t^2)+3(t^3+t^2+t)+4(t^3+t^2+t+1)
\end{align}
