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## Homework Statement

Find the eigenvalues and eigenvectors of the following matrix: $$ A = \begin{bmatrix}

3 & 0 & 0 \\

0 & 3 & 2 \\

0 & -1 & 0

\end{bmatrix}

$$

## Homework Equations

Characteristic polynomial: $$ \Delta (t) = t^3 - Tr(A) t^2 + (A_{11}+A_{22} +A_{33})t - det(A) .$$

## The Attempt at a Solution

From the characteristic polynomial equation above, I've found the characteristic polynomial of the matrix and then I'd found the eigenvalues: $$ \lambda_1 = 2 \\ \lambda_2 = \frac {7 + \sqrt {61}} {2} \\ \lambda_3 = \frac {7 - \sqrt {61}} {2} .$$

But these values of ##\lambda## are too strange though. I've tried to calculate this using Mathway calculator, but there aren't no answer for this problem there. I think this problem hasn't a solution. What do you guys think about it?