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My matrix is $A=\begin{pmatrix}0 & 0 & -2\\ 1 & 2 & 0 \\ 0 & -2 & 0\end{pmatrix}$

I have to find its eigenvalues and eigenvectors but characteristic polynomial is $3$rd degree and I can't calculate it. Please give a help for it. Thanks.

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    as i understood,there is no way without making these calculations.i thought maybe there could be a different way to find eigenvectors. ok. thank you.2012-11-12

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The eigenvalues of a matrix A are the solutions $\lambda$ to the equation of the form $det(A-\lambda I)$. Det refers to the determinant of the matrix formed by $(A - \lambda I)$ and I is the $n$ x $n$ identity matrix -- this is called the characteristic equation. To find your eigenvalues and eigenvectors just find the solution using $det(A-\lambda I)$. If you need me to elaborate any further just ask.

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    @aicha If you need help with the commands just ask.2012-11-12