I need to know how to compute T with respect to the basis b. and i need a way to know where b is a basis consisting of egeinvectors of T.

Let v= p_1(R), T(a+bx)= (6a-6b)+(12a-11b)x and the basis B={3+4x,2+3x}

Let V= R^3, T =$\displaystyle \begin{pmatrix}\ a \\ b \\ c\end{pmatrix}\$ = $\displaystyle \begin{pmatrix}\ 3a + 2b - 2c\\ -4a-3b+2c\\-c\end{pmatrix}\$

The basis B= { $\displaystyle \begin{pmatrix}\ 0 \\ 1 \\ 1\end{pmatrix}\$ $\displaystyle \begin{pmatrix}\ 1 \\ -1 \\ 0\end{pmatrix}\$ $\displaystyle \begin{pmatrix}\ 1 \\ 0 \\ 2 \end{pmatrix}\$ }

general steps will defenitely help.