Let \(A=\left[\begin{array}{rrr}1 & 1 & 2 \\ 1 & -2 & 5 \\ 2 & 5 & -3\end{array}\right]\) Then the eigenvalues of A are 

1
-4, 3, -3 
2
4, 3, 1 
3
4, -4±√13
4
4, -2±2√7

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