GATE | GATE CS 2011 | Question 40

Consider the matrix as given below.

GATECS2011Q40

Which one of the following options provides the CORRECT values of the eigenvalues of the matrix?
(A) 1, 4, 3
(B) 3, 7, 3
(C) 7, 3, 2
(D) 1, 2, 3


Answer: (A)

Explanation:

The Eigen values of a triangular matrix are given by its diagonal entries. We can also calculate (or verify given answers) using characteristic equation obtained by |M – λI| = 0.

 

1-λ    2     3

0     4-λ    7           =       0

0      0     3-λ 

Which means

(1-λ)(4-λ)(3-λ) = 0


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