TIFR ECE 2015 | Question: 13

Question

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

• A. only negative eigenvalues
• B. only non-zero eigenvalues
• C. only positive eigenvalues
• D. one negative and one positive eigenvalue
• E. None of the above