GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 27 of 65

Marks: +1, -0

Consider the matrix

P=[\table 1 , 1 , 0 ; 0 , 1 , 1 ; 0 , 0 , 1 ]

The number of distinct eigenvalues of

P

Solution:

The characteristic equation of matrix P which satisfies

|P − λI| = 0

So,

|[\table 1 , 1 , 0 ; 0 , 1 , 1 ; 0 , 0 , 1]-λ[\table 1 , 0 , 0 ; 0 , 1 , 0 ; 0 , 0 , 1]|=0

|\table 1-λ , 1 , 0 ; 0 , 1-λ , 1 ; 0 , 0 , 1-λ|=0

Or,

(1-λ)[(1-λ)(1-λ)-0]=0

⇒ λ=1,1,1

Therefore, no. of distinct eigen values

=1

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