How to find a matrix for linear transformation? $T: \mathbb R^2[x] \to \mathbb R^2[x]$ is given with the regulation: $(Tp)(x) = (xp(x))'$ If $q(x) = 1 - x + x^2$, what is T*(q)? I don't understand what the left side of the regulation means and how to get a matrix from the regulation, also I apologize for the poor formatting. Edit: The asterisk sign should be above T in the question with q, as in adjugate matrix.

**Hint**

The transformation $T$ is acting on the polynomial $p(x)$ to give the output as the derivative of $xp(x)$. For example, $T(x)=\frac{d}{dx}(x^2)=2x$ and so on.

To get the matrix you should determine the behavior of the transformation $T$ on a basis like $\\{1,x,x^2\\}$.