Question

The eigen values of matrix $\left[\begin{array}{cc}9& 5\\ 5& 8\end{array}\right]$ are

• A. -2.42 and 6.86
• B. 3.48 and 13.53
• C. 4.70 and 6.86
• D. 6.86 and 9.50

Answer 1

The correct option is B 3.48 and 13.53

The characteristic equation of given matrix A is $|A-\lambda I|=0$
$\left|\begin{array}{cc}9-\lambda & 5\\ 5& 8-\lambda \end{array}\right|=0$
$\Rightarrow (9-\lambda )(8-\lambda )=25$
$\Rightarrow \lambda =3.48,13.53$

Alternate method
Property : 'Sum of eigen values=trace (A)' is satisfied by only (b)