- #1

Bucky

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## Homework Statement

Find the eigenvalues and eigenvectors of

[itex]

A = \left(\begin{array}{ccc}5&1&1\\1&3&1\\1&1&3\end{array}\right)

[/itex]

## The Attempt at a Solution

The problem I'm having is finding the eigenvalues for the matrix. In 2d matricies it's not too bad, but in 3d the determinant is quite big, and I end up with

[itex] -\lambda^3 - \lambda^2 - 20\lambda + 34 = 0 [/itex]

*(note - very possible this is wrong, there's enough numbers being pushed around for something to have went wrong.)*

How do I get three roots from this? Taking the values given in the book I get the rest of the question, it's just this step that's giving me trouble.

Thanks.

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