$B=\{1,1+x,1+x+x^2\}, C=\{1+x,2x,x^2-1\}$
$B$ and $A$ are both bases for the polynomial space $P_2[x]$.
$T: P_2[x] \to P_2[x]$
$$[T]B = \begin{pmatrix} 3 & 3 & 3\\ -2 & -6 & -6\\ 1 & 5 & 6 \end{pmatrix} $$
Find $[T(2x^2 +2x+1)]_C$
This is the full question but in Hebrew, you can see the matrix and the bases there as well.
