Question

The lowest eigen value of the 2 x 2 matrix $\left[\begin{array}{cc}4& 2\\ 1& 3\end{array}\right]$ is .

• A. 2

Answer 1

The correct option is A 2
$A=\left[\begin{array}{cc}4& 2\\ 1& 3\end{array}\right]$
Characteristic equation is $|A-\lambda I|=0$

$\left|\begin{array}{cc}4-\lambda & 2\\ 1& 3-\lambda \end{array}\right|=0$
$(4-\lambda )(3-\lambda )-2=0$
$12-4\lambda -3\lambda +{\lambda }^2-2=0$
${\lambda }^2-7\lambda +10=0$
$\lambda =2,5$

Lowest eigen value is 2.