GATE2010 q29 Revision as of 17:38, 15 April 2014 by Arjun Suresh (talk | contribs) (Created page with "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...") (diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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.

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