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I have a problem. There is a linear trasformation [tex]\xi:\mathbb{R}^2\mapsto\mathbb{R}^2[/tex] and:

[tex]\xi\begin{pmatrix}3\\1\end{pmatrix}=\begin{pmatrix}2\\-4\end{pmatrix}[/tex]

[tex]\xi\begin{pmatrix}1\\1\end{pmatrix}=\begin{pmatrix}0\\2\end{pmatrix}[/tex]

How to find a matrix for this linear transformation for basis [tex]\mathcal{B}=\left\{\begin{pmatrix}1\\2\end{pmatrix},\begin{pmatrix}2\\1\end{pmatrix}\right\}[/tex]

Thank you so much :-)