Question

The eigen values of the matrix A = $\left[\begin{array}{ccc}1& -1& 5\\ 0& 5& 6\\ 0& -6& 5\end{array}\right]$ are

• A. 1, 5, 6
• B. 1, -5, $\pm$j6
• C. 1, 5$\pm$j6
• D. 1, 5, 5

Answer 1

The correct option is C 1, 5$\pm$j6

Characteristic equation is $\left|\begin{array}{ccc}1-\lambda & -1& 5\\ 0& 5-\lambda & 6\\ 0& -6& 5-\lambda \end{array}\right|$ = 0

$\Rightarrow$ $(1-\lambda )\left[\right(5-\lambda {)}^2+36]$ = 0

$\lambda =1,{\lambda }^2-10\lambda +61=0\Rightarrow \lambda$ = 1 and $\lambda =5$ $\pm$ j6