Matrix/2 0 5 0 -1 0 8 0 5/Eigenspaces/Exercise

Determine the eigenvalues and the eigenspaces of the linear mapping

$\varphi \colon \mathbb {R} ^{3}\longrightarrow \mathbb {R} ^{3},v\longmapsto Mv,$

given by the matrix

${}M={\begin{pmatrix}2&0&5\\0&-1&0\\8&0&5\end{pmatrix}}\,.$

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