Define $\alpha \in End(\mathbb{R}^3)$ by $\alpha: \begin{bmatrix} a\\ b\\ c \end{bmatrix} \mapsto \begin{bmatrix} a-b\\ a+2b+c\\ -2a+b-c \end{bmatrix}$. Find the eigenvalues of $\alpha$ and, for each eigenvalue, find the associated eigenspace.
2026-03-28 04:00:51.1774670451
find the eigenvalues find the associated eigenspace
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