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”

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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