Linear mapping/Standard basis/(5 1 2 3)/Matrix with respect to 1 4 and 4 2/Exercise

Let ${}\varphi \colon \mathbb {R} ^{2}\rightarrow \mathbb {R} ^{2}$ be the linear mapping determined by the matrix ${}M={\begin{pmatrix}5&1\\2&3\end{pmatrix}}$ (with respect to the standard basis). Determine the describing matrix of ${}\varphi$ with respect to the basis ${}{\begin{pmatrix}1\\4\end{pmatrix}}$ and ${}{\begin{pmatrix}4\\2\end{pmatrix}}$.

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