Given $\beta = ${$1,x^2,x$} and $\gamma = ${$(1,1), (1,0)$},
$T: P^2(\Bbb{R}) \to \Bbb{R}^3 $ is $ T(a + bx + cx^2) = (a + b, a + c)$, calculate $[T]_\beta^\gamma$.
I just need confirmation that I'm not crazy and that there is a typo - the transformation maps to $\Bbb{R}^2$ right?
And how do I calculate $[T]_\beta^\gamma$? I've never been good at this. Do I transform it through $\beta$ then $\gamma$?
Edit: After tips from Lem.ma, I got
$T(1) = (1,1) = 1(1,1) + 0(1,0)$
$T(x^2) = (0,1) = 1(1,1) + -1(1,0)$
$T(x) = (1,0) = 0(1,1) + 1(1,0)$
So, $[T]_\beta^\gamma$ = $\begin{bmatrix} 1&1&0\\0&-1&1 \end{bmatrix}$ ?