What are the eigenvalues of the following $2\times 2$ matrix? $$\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$$
Let the eigen values be $a,b$
Sum of Eigen Values = Trace(Diagonal Sum)
$\implies a+b = 2+5 = 7$
Product of Eigen Values = Det(A)
$\implies a\times b = 6$
Solving these we get eigenvalues as 1 and 6.
Option(B) is Correct.
@shamim_ahmed how you are getting 2 & 5,
characteristic equation will be let lambda = x x^{2 } -7x+6=0 if you solve this equation you will get (1,6) or follow the above method ..!
Gatecse
It's a test series conducted by Kiran sir i.e...