Linear map given on a basis of R2

Let $T:\mathbb R^2\to\mathbb R^2$ be a linear transformation such that $T\left(\begin{bmatrix}1\\2\end{bmatrix}\right)=\begin{bmatrix}1\\0\end{bmatrix}$ and $T\left(\begin{bmatrix}2\\1\end{bmatrix}\right)=\begin{bmatrix}0\\1\end{bmatrix}$. Suppose that $\begin{bmatrix}3\\-2\end{bmatrix}=\alpha\begin{bmatrix}1\\2\end{bmatrix}+\beta\begin{bmatrix}2\\1\end{bmatrix}$ and $T\left(\begin{bmatrix}3\\-2\end{bmatrix}\right)=\begin{bmatrix}a\\b\end{bmatrix}$. Then $\alpha+\beta+a+b$ equals