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GATE | GATE IT 2006 | Question 26

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What are the eigenvalues of the matrix P given below
 \begin{pmatrix}    a     & 1     & 0\\    1     & a     & 1 \\   0     & 1     &a \end{pmatrix} (A) a, a -√2, a + √2 (B) a, a, a (C) 0, a, 2a (D) -a, 2a, 2a

Answer: (A)

Explanation: det(A-λ.I))=0 (a-λ)*[(a-λ)2-1] -1*(a-λ)= 0 (a-λ)3 – 2(a-λ) = 0 (a-λ)((a-λ)2 – 2) = 0 (a-λ)(a-λ+√2)(a-λ-√2) = 0

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Last Updated : 28 Jun, 2021
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