GATE | GATE-CS-2005 | Question 49

What are the eigenvalues of the following 2 × 2 matrix?

GATECS2005Q49
(A) -1 and 1
(B) 1 and 6
(C) 2 and 5
(D) 4 and -1


Answer: (B)

Explanation: The eigenvalues of A are precisely the real numbers λ that satisfy the equation det(A – &lambda I) = 0.

Let us find determinant value of A – &lambda I;



2-λ     -1
   -4       5-λ   

We get the equation as λ2 -7 λ + 6 = 0 which gives us eigenvalues as 6 and 1.

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