Let \(\mathcal {B}=\left \{ \begin{bmatrix}1\\1\\0\end{bmatrix}, \begin{bmatrix}1\\2\\0\end{bmatrix}, \begin{bmatrix}0\\1\\2\end{bmatrix}\right \}\) be an ordered basis for \(\RR ^3\). (Mentally verify that \(\mathcal {B}\) is a basis of \(\RR ^3\).)

Let \(\vec {v}=\begin{bmatrix}-1\\-3\\2\end{bmatrix}\) be a vector of \(\RR ^3\) (written with respect to the standard basis of \(\RR ^3\)). Find the coordinate vector for \(\vec {v}\) with respect to \(\mathcal {B}\).

\[\begin{bmatrix}\answer {2}\\\answer {-3}\\\answer {1}\end{bmatrix}\]