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(a) Find the eigenvalues and corresponding eigenvectors of the following matrix: 0-4 A = 0 5 4 -4 4 3 ·( X₁ = [1, -2]T, and A₂ = -3 with eigenvector X₂ = [1,-1]. 1 If P is a matrix such that P = ( X₁ X₂ ) = (-¹/2-¹₁), s show that P-¹AP -1 gives a diagonal matrix with the same eigenvalues as A. (b) The matrix A = -5-2 has eigenvalues X₁ = -1 with eigenvector 1

(a) Find the eigenvalues and corresponding eigenvectors of the following matrix: 0-4 A = 0 5 4 -4 4 3 ·( X₁ = [1, -2]T, and A₂ = -3 with eigenvector X₂ = [1,-1]. 1 If P is a matrix such that P = ( X₁ X₂ ) = (-¹/2-¹₁), s show that P-¹AP -1 gives a diagonal matrix with the same eigenvalues as A. (b) The matrix A = -5-2 has eigenvalues X₁ = -1 with eigenvector 1

Elementary Linear Algebra (MindTap Course List)
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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(a) Find the eigenvalues and corresponding eigenvectors of the following matrix: 0-4 A = 05 -4 4 4 3 (b) The matrix A = ·( |has eigenvalues A₁ = -1 with eigenvector X₁ = [1, -2]T, and A₂ = -3 with eigenvector X₂ = [1,-1]T. 1 If P is a matrix such that P = ( X₁ X₂ ) = (-¹/₂2 - ₁1), s -1 gives a diagonal matrix with the same eigenvalues as A. -5-2 1 show that P-¹AP
Transcribed Image Text:(a) Find the eigenvalues and corresponding eigenvectors of the following matrix: 0-4 A = 05 -4 4 4 3 (b) The matrix A = ·( |has eigenvalues A₁ = -1 with eigenvector X₁ = [1, -2]T, and A₂ = -3 with eigenvector X₂ = [1,-1]T. 1 If P is a matrix such that P = ( X₁ X₂ ) = (-¹/₂2 - ₁1), s -1 gives a diagonal matrix with the same eigenvalues as A. -5-2 1 show that P-¹AP
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