Constants: a = 2, b = 3 The following statements are TRUE. Explain why. a. If the characteristic polynomial of a matrix M is χ(λ) = (λ)(λ − 2)(λ + 2), then M is diagonalizable. b. If M is a 5 × 5 matrix with eigenvalues 1, 4, and −5, and the dimension of λ = 4 eigenspace is 3, then M is diagonalizable. d. The eigenvalues of an upper triangular matrix are the entries along the main diagonal.

Constants: a = 2, b = 3 The following statements are TRUE. Explain why. a. If the characteristic polynomial of a matrix M is χ(λ) = (λ)(λ − 2)(λ + 2), then M is diagonalizable. b. If M is a 5 × 5 matrix with eigenvalues 1, 4, and −5, and the dimension of λ = 4 eigenspace is 3, then M is diagonalizable. d. The eigenvalues of an upper triangular matrix are the entries along the main diagonal.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CR: Review Exercises

Problem 15CR: For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of...

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