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Find the eigenvalues and eigenvectors of the linear operator \(\hat{A}\), represented by the matrix

\[ 
A=\left(\begin{array}{ccc}
-1 & 1 & 1 \\
1 & -5 & 1 \\
1 & 1 & -2 
\end{array}\right)
\]

Will the eigenvectors be orthogonal?

Present the answer in LaTex format: \boxed{Your answer}
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