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Would someone please explain to me how I can find eigenvalues and eigenvectors by inpection of simple symmetric matrices? I just can't figure it out.

He is an example:

By looking at [tex]A=\left(\begin{matrix}2&-1&-1\\-1&2&-1\\-1&-1&2\end{matrix}\right)

[/tex] I should be able to guess that [1,1,1] is an eigenvector.

He is an example:

By looking at [tex]A=\left(\begin{matrix}2&-1&-1\\-1&2&-1\\-1&-1&2\end{matrix}\right)

[/tex] I should be able to guess that [1,1,1] is an eigenvector.

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