# Matrix/3 5 0 3/Jordan/Exercise

Suppose that a linear mapping

is given by the matrix

with respect to the standard basis. Find a basis, such that is described by the matrix

with respect to this basis.

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.