I have a question to do with linear algebra.
Consider the linear map $T:\mathbb{R}[x]\le _2 \to\mathbb{R}^2$, given by the matrix:
$ \begin{pmatrix} 1 & 1 & 2\\ 2 & 0 & 3 \end{pmatrix} $ (sorry for my terrible formatting but it's my first time posting. This is referring to the set of continuous functions with degree less than or equal to 2.)
Find the linear map with respect to the coordinate system $\begin{pmatrix}1 & x & x^2\\\end{pmatrix}$:$\mathbb{R}^3\to\mathbb{R}[x]\le _2$ (and the standard coordinate system $id:\mathbb{R}^2\to\mathbb{R}^2$).