Question

The eigen values of the matrix $\left[\begin{array}{cc}4& -2\\ -2& 1\end{array}\right]$ are

• A. $1$ and $4$
• B. $-1$ and $2$
• C. $0$ and $5$
• D. Cannot be determined

Answer 1

The correct option is C $0$ and $5$

$A=\left[\begin{array}{cc}4& -2\\ -2& 1\end{array}\right]$
$|A-\lambda I|=0$
$\Rightarrow \left[\begin{array}{cc}4-\lambda & -2\\ -2& 1-\lambda \end{array}\right]=0$
$(4-\lambda )(1-\lambda )-4=0$
$4-5\lambda +{\lambda }^2-4=0$
$\lambda =0,5$
Not: Here, sum of eigen values = trace (A) is satisfied by (a) & (c). Hence we have to solve the characteristic equatuon