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(a) T F: Any non-zero vector u e R" is an eigenvector of A = uu". (b) T F: For any n x n permutation matrix P, x = (1,1,..., 1) € R" is an eigenvector of P. (c) T F: If 0 is an eigenvalue of an n x n matrix A, then N(A) = {0}.

(a) T F: Any non-zero vector u e R" is an eigenvector of A = uu". (b) T F: For any n x n permutation matrix P, x = (1,1,..., 1) € R" is an eigenvector of P. (c) T F: If 0 is an eigenvalue of an n x n matrix A, then N(A) = {0}.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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True or False? Circle your answer and provide a justification for your choice. (a) T F: Any non-zero vector u e R" is an eigenvector of A = uu". (b) T F: For any n x n permutation matrix P, x = (1, 1,..., 1) E R" is an eigenvector of P. (c) T F: If 0 is an eigenvalue of an n x n matrix A, then N(A) = {0}. (d) T F: If A is an eigenvalue of a square matrix A, then every non-zero element in N(A – AI) is an eigenvector of A with eigenvalue A. (e) T F: If A is an eigenvalue of an n x n matrix A and u is an eigenvalue of an n x n matrix B, then Au is an eigenvalue of AB.
Transcribed Image Text:True or False? Circle your answer and provide a justification for your choice. (a) T F: Any non-zero vector u e R" is an eigenvector of A = uu". (b) T F: For any n x n permutation matrix P, x = (1, 1,..., 1) E R" is an eigenvector of P. (c) T F: If 0 is an eigenvalue of an n x n matrix A, then N(A) = {0}. (d) T F: If A is an eigenvalue of a square matrix A, then every non-zero element in N(A – AI) is an eigenvector of A with eigenvalue A. (e) T F: If A is an eigenvalue of an n x n matrix A and u is an eigenvalue of an n x n matrix B, then Au is an eigenvalue of AB.
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