Difference between revisions of "GATE2010 q29"

Latest revision as of 11:51, 15 July 2014

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

Solution by Happy Mittal

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.