Let $V$ be the space spanned by the two functions $\cos(t)$ and $\sin(t)$. Find the matrix $A$ of the linear transformation T(f(t)) = f''(t) + 7f'(t) + 4f(t) from $V$ into itself with respect to the basis $\{\cos(t), \sin(t)\}$.
$A = \left[\begin{matrix}\color{red}{\square} & \color{red}{\square} \\ \color{red}{\square} & \color{red}{\square} \end{matrix}\right]$
I don't know where to start. Where does A go in regards to the $T(f(t))=\ldots$ equation?