Question

The eigen values of the matrix $\left[\begin{array}{cc}5& 3\\ 2& 9\end{array}\right]$ are,

• A. $(5.13,9.42)$
• B. $(3.85,2.93)$
• C. $(9.00,5.00)$
• D. $(10.16,3.84)$

Answer 1

The correct option is D $(10.16,3.84)$

For eigen values
$|A-\lambda I|=0$
$\Rightarrow \left[\begin{array}{cc}5-\lambda & 3\\ 2& 9-\lambda \end{array}\right]=0$
$\Rightarrow (5-\lambda )(9-\lambda )-6=0$
${\lambda }^2-14\lambda +39=0$
$\lambda =\frac{14\pm \sqrt{196-156}}{2\left(1\right)}$
$\lambda =\frac{14\pm 2\sqrt{10}}{2}=7\pm \sqrt{10}$
$\lambda =10.16,3.84$