Question

Eigen values of the following matrix are: $\left[\begin{array}{cc}-1& 4\\ 4& -1\end{array}\right]$

• A. $3$ and $-5$
• B. $-3$ and $5$
• C. $-3$ and $-5$
• D. $3$ and $5$

Answer 1

The correct option is A $3$ and $-5$

For eigen vaues
$|A-\lambda I|=0$
$\Rightarrow \left[\begin{array}{cc}-1-\lambda & 4\\ 4& -1-\lambda \end{array}\right]=0$
$(-1-\lambda {)}^2-16=0$
${\lambda }^2+2\lambda -15=0$
$\lambda =-5,3$
Alternative Solution
Sum of eigen values = trace (A)
This property is satisfied by only (a)