Gate2017 ss Q42

42If the characteristic polynomial of a 3 × 3 matrix M over R (the set of real numbers) is λ³ – 4λ² + aλ + 30, where a ∈ R, and one eigen value of M is 2, then the largest among the absolute values of the eigenvalues of M is _______

Note: Numerical Type question.

Option : D
Explanation :
Since one eigen value of M is 2 thus it satisfies the characteristics equation so
∴ 2³ - 4(2)² + a(2) + 30 = 0
⇒ a = -11
∴ Charcteristic polynomial is
λ³ - 4λ² - 11λ + 30 = 0
(λ - 2)(λ - 5)(λ + 3) = 0
∴ λ=2,5,-3
Largest absolute value of 'λ' is 5

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