I've been staring at this problem for over an hour, trying different things and getting approximately nowhere. Here's the problem:
Let $w_1=\begin{bmatrix}1\\2\\0\end{bmatrix},w_2=\begin{bmatrix}2\\5\\1\end{bmatrix}, w_3=\begin{bmatrix}2\\4\\1\end{bmatrix}$ Let $f:\mathbb{R}^3\rightarrow\mathbb{R}^3$ be the linear transformation satisfying: $f(w_1)=w_2-w_3,f(w_2)=-w_2+w_3,f(w_3)=w_1+w_2+w_3$ Give the matrix representation of $f$ with respect to the basis {$w_1,w_2,w_3$}. Also give the matrix representation of $f$ where the input x is written with respect to the basis {$w_1,w_2,w_3$} and the output $f(x)$ is written with respect to the standard basis.
It's coming up with the matrix representation that's getting me—I think once I have that I can probably figure out how to find the one that shows the output with respect to the standard basis. I just have no idea how to even get started and I can't find anything that looks like this problem in my textbook.
Even just a hint on how to get started would be awesome.