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Mathematics - Matrices Question with Solution | TestHub

MathematicsMatricesCharacteristics EquationHard2 minQB

MathematicsHardmultiple choice

Matrix $A$ has Row 1: 1, 1, 0; Row 2: 2, 2, 1; Row 3: 0, 1, -1. If $A^{3} - 2 A^{2} + λ A + I = O$ , which are true?

Options:(select one or more)

Answer:

B, C

Solution:

The characteristic equation is $x^{3} - 2 x^{2} - 4 x + 1 = 0$ , so $λ = - 4$ . It also gives $A^{2} + A^{- 1} = 2 A + 4 I$ , whose determinant is 56.

Stream:JEESubject:MathematicsTopic:MatricesSubtopic:Characteristics Equation

⏱ 2mℹ️ Source: QB

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