linear transformation with transformation matrix

Question

Let $C=(w_1, w_2)$ and $B=(v_1, v_2)$ be basis of $R^2$.

$u \in R^2$.

and: $[T]_C^B=$ $$ \begin{matrix} 1 & -2 \\ -3 & 5 \\ \end{matrix} $$

$T(T(u))=w_1+2w_2$

$v_1=(1 \space 5)^T$ $v_2=(-3 \space 1)^T$

What is $T(u)$?

Answer 1

Hint: The inverse of the given matrix is $[T^{-1}]^C_B$, and multiply it by $(1,2)^T$ to get the coordinates of $T(u)$ in basis $B$.