GATE | GATE-CS-2017 (Set 2) | Question 65

If 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: This question appeared as Numerical Answer Type.
(A) 2
(B) 3
(C) 4
(D) 5


Answer: (D)

Explanation: λ3 – 4λ2 + aλ + 30 = 0
Since 2 is root . putting in eqn we get a = -11
λ3 – 4λ2 – 11λ + 30 =0
solving we get λ = 2, -3, 5.

Refer http://quiz.geeksforgeeks.org/eigen-values-and-eigen-vectors/ for details.

Quiz of this Question



My Personal Notes arrow_drop_up