Matrix/ 2 3 4 0 2 5 0 0 2/Jordan/Exercise

We consider the linear mapping

$\varphi \colon \mathbb {R} ^{3}\longrightarrow \mathbb {R} ^{3}$

that is described, with respect to the standard basis, by the matrix

${\begin{pmatrix}2&3&4\\0&2&5\\0&0&2\end{pmatrix}}.$

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

${\begin{pmatrix}2&1&0\\0&2&1\\0&0&2\end{pmatrix}}.$

Create a solution