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Let

\[

A=\left(\begin{array}{ccc}

1 & 1+\varepsilon & 1 \\

1+\varepsilon & 1 & 1+\varepsilon \\

1 & 1+\varepsilon & 1

\end{array}\right)

\]

Then for $\varepsilon=10^{-6}, A$ has

- only negative eigenvalues
- only non-zero eigenvalues
- only positive eigenvalues
- one negative and one positive eigenvalue
- None of the above