find a non diagonizable 3x3 matrix with precisely one real eigenvalue of multiplicity 1

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Question: find a non diagonizable 3x3 matrix with precisely one real eigenvalue of multiplicity 1?

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The jordan-block $$\begin{pmatrix}1&1&0\\0&1&1\\0&0&1\end{pmatrix}$$ is not diagonizable and has one real eigenvalue namely $1$ with multiplicity 1.