Let : IRn → IRn be a linear operator whose characteristic polynomial of T e: pT (λ) = λ (λ2 − 1) (λ − 2)3 Rate as true (T) or false (F): (I) T and one-to-one linear transformation. (II) The algebraic multiplicity of the eigenvalue 1, ma(1), is equal to 2. (III) T and surjective linear transformation

Let : IRn → IRn be a linear operator whose characteristic polynomial of T e: pT (λ) = λ (λ2 − 1) (λ − 2)3 Rate as true (T) or false (F): (I) T and one-to-one linear transformation. (II) The algebraic multiplicity of the eigenvalue 1, ma(1), is equal to 2. (III) T and surjective linear transformation

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 16CM

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Question

Let : IRⁿ→ IRⁿ be a linear operator whose characteristic polynomial of T e:

pT (λ) = λ (λ² − 1) (λ − 2)³

Rate as true (T) or false (F):

(I) T and one-to-one linear transformation.

(II) The algebraic multiplicity of the eigenvalue 1, ma(1), is equal to 2.

(III) T and surjective linear transformation.

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