A Linear transformation $L$ in $\mathbb R^3$ with matrix $$ L_b^b = \left(\begin{matrix} 1 & 0 & 5 \\ 0 & -2 & 2 \\ 1 & -2 & 7 \end{matrix}\right)$$ and basis $b = \{ (1,0,2), (0,2,1), (1,3,1) \}$ find $L(2,0,5)$
my first guess was $L * \left(\begin{matrix}2\\0\\5\end{matrix}\right)$ which would be $\left(\begin{matrix}27\\10\\37\end{matrix}\right)$ but I'm confused since I did not use the basis anywhere... is it given as extra info to confuse me, or did I mess up?