Chapter 3.SE, Problem 10SE

Let $B=\{x_1,x_2\}$ be a basis for $R^2$ and let $T:R^2\to R^2$ be a linear transformation such that

$T\left(x_1\right)=\left[\begin{array}{c}1\\ 1\end{array}\right]$ and $T\left(x_2\right)=\left[\begin{array}{c}2\\ -1\end{array}\right]$.

If $e_1=x_1-2x_2$ and $e_2=2x_1+x_2$, where $e_1$ and $e_2$ are the unit vectors in $R^2$, then find the matrix of $T$.