Matrix/-2 2 7 0 -2 -6 0 0 -2/Jordan/Exercise

Suppose that the linear mapping

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

is given by the matrix

${\begin{pmatrix}-2&2&7\\0&-2&-6\\0&0&-2\end{pmatrix}}$

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

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

with respect to the new basis.

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