Change of bases - linear transformation

Question

Let $f:R^2→R^2$ be the linear transformation defined by $f(x)$=$$(\begin{matrix}3 & -3\\0 & -3 \\\end{matrix})x $$.

Let $B = {⟨1,−2⟩,⟨3,−7⟩}, C = {⟨1,−1⟩,⟨−3,2⟩}$, be two different bases for $R^2$. Find the matrix for $f$ relative to the basis $B$ in the domain and $C$ in the codomain.

I do not understand the wording... what does it mean by ''...to the basis B in the domain and C in the codomain?"" Does it just mean $R^2$ for both?

Answer 1

$f(B_1)=(9,6)=-36C_1-15C_2$

$f(B_2)=(30,21)=-123C_1-51C_2 $

So the matrix is $$\begin{bmatrix} -36 & -123 \\ -15 & -51 \end{bmatrix} $$