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Return to GATE2010 q29.
Consider the following matrix $$A = \left[\begin{array}{cc}2 & 3\\x & y \end{array}\right]$$ If the eigenvalues of A are 4 and 8, then
(A) x = 4, y = 10
(B) x = 5, y = 8
(C) x = -3,y = 9
(D) x = -4, y = 10
Characteristic equation for given matrix is $$(2-λ)(y-λ)-3x = 0$$ Putting λ = 4 and 8, we get 2 equations : $$3x+2y = 8$$ $$3x+6y = 48$$ Solving both equations, we get x = -4, y = 10. So option (D) is correct.
GATECSE