Question

The eigen value of the matrix $\left[P\right]=\left[\begin{array}{cc}4& 5\\ 2& -5\end{array}\right]$ are

• A. -7 and 8
• B. -6 and 5
• C. 3 and 4
• D. 1 and 2

Answer 1

The correct option is B -6 and 5

$\left[P\right]=\left[\begin{array}{cc}4& 5\\ 2& -5\end{array}\right]$ its eigen values are given by

$|P-\lambda I|=\left|\begin{array}{cc}4-\lambda & 5\\ 2& -5-\lambda \end{array}\right|=0$
$\Rightarrow (4-\lambda )(-5-\lambda )-10=0$
$=(\lambda +5)(\lambda -4)-10=0$
$={\lambda }^2+\lambda -20-10=0$
$=(\lambda +6)(\lambda -5)=0$
$\lambda =-6,5$

Note : Only (b) satifies sum of eigen values = trace of P.(trick for Exam)