Answered: V n-dimensional vector space T: V → V…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 74E

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V n-dimensional vector space T: V → V Let it be the linear transformation. Let the eigenvalue of this linear transformation be λ and the eigenvector corresponding to this eigenvalue x ≠ 0 So which of the following is true?

a)There is only one λ value corresponding to the vector X.

b)There is an infinite eigenvector for λ eigenvalue

c)linear transform has real eigenvalue as much as the degree of the characteristic polynomial

d)The matrix representation of the linner transformation is the invertible matrix A and the eigenvalue of A^-1 is λ^-1 ,with an eigenvalue λ^.

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