Question

Eigen values of the Matrix $\left[\begin{array}{ccc}3& -1& -1\\ -1& 3& -1\\ -1& -1& 3\end{array}\right]$ are

• A. 1, 1, 1
• B. 1, 1, 2
• C. 1, 4, 4
• D. 1, 2, 4

Answer 1

The correct option is C 1, 4, 4

$\because$ Sum of eigen values = Trace (A)

$\Rightarrow$ ${\lambda }_1+{\lambda }_2+{\lambda }_3$ = 9

Only option (c) is satisfying it