Matrix/3 5 0 3/Jordan/Exercise

Suppose that a linear mapping

$\varphi \colon \mathbb {R} ^{2}\longrightarrow \mathbb {R} ^{2}$

is given by the matrix

${\begin{pmatrix}3&5\\0&3\end{pmatrix}}$

with respect to the standard basis. Find a basis, such that ${}\varphi$ is described by the matrix

${\begin{pmatrix}3&1\\0&3\end{pmatrix}}$

with respect to this basis.

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