1 0 0 Let A = -3 1 3 3 0-2 (a) Find all eigenvalues of A. (b) For each eigenvalue A of A, find a basis of the eigenspace Nul (AI - A). (c) If possible, diagonalize A; that is, find an invertible matrix PE R3×3 and a diagonal matrix D = R³×³ such that A = PDP-¹. (d) Given a positive integer k, compute and simplify A.
1 0 0 Let A = -3 1 3 3 0-2 (a) Find all eigenvalues of A. (b) For each eigenvalue A of A, find a basis of the eigenspace Nul (AI - A). (c) If possible, diagonalize A; that is, find an invertible matrix PE R3×3 and a diagonal matrix D = R³×³ such that A = PDP-¹. (d) Given a positive integer k, compute and simplify A.
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 80E
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