Question

The minimum eigen value of the following matrix is $$\left[\begin{array}{ccc}3& 5& 2\\ 5& 12& 7\\ 2& 7& 5\end{array}\right]$$

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is A 0

Characteristic equation is $|A-\lambda I|=0$
$\left|\begin{array}{ccc}3-\lambda & 5& 2\\ 5& 12-\lambda & 7\\ 2& 7& 5-\lambda \end{array}\right|=0$

$\Rightarrow {\lambda }^3-20{\lambda }^2+33\lambda =0$
$\lambda =0,10\pm \sqrt{67}$
So minimum eigen value is 0