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True/False: If the statement is false, justify why it is false. (a) If a matrix is invertible, then it is diagonalizable. 1 2 -1 2 04-3 00 3 2 2 00 0 -2, (b) 2 is an eigenvalue of A = (c) If Ax = Xx for some vector x, then A is an eigenvalue of A. (d) If λ + 2 is a factor of the characteristic polynomial of A, then 2 is an eigenvalue of A. (e) In order for an n x n matrix A to be diagonalizable, A must has n distinct eigenvalues.

True/False: If the statement is false, justify why it is false. (a) If a matrix is invertible, then it is diagonalizable. 1 2 -1 2 04-3 00 3 2 2 00 0 -2, (b) 2 is an eigenvalue of A = (c) If Ax = Xx for some vector x, then A is an eigenvalue of A. (d) If λ + 2 is a factor of the characteristic polynomial of A, then 2 is an eigenvalue of A. (e) In order for an n x n matrix A to be diagonalizable, A must has n distinct eigenvalues.

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/False: If the statement is false, justify why it is false. (a) If a matrix is invertible, then it is diagonalizable. 1 2 -1 2 04-3 2 2 (b) 2 is an eigenvalue of A = 00 3 00 0 -2, (c) If Ax = Xx for some vector x, then A is an eigenvalue of A. (d) If X + 2 is a factor of the characteristic polynomial of A, then 2 is an eigenvalue of A. (e) In order for an n x n matrix A to be diagonalizable, A must has n distinct eigenvalues.
Transcribed Image Text:True/False: If the statement is false, justify why it is false. (a) If a matrix is invertible, then it is diagonalizable. 1 2 -1 2 04-3 2 2 (b) 2 is an eigenvalue of A = 00 3 00 0 -2, (c) If Ax = Xx for some vector x, then A is an eigenvalue of A. (d) If X + 2 is a factor of the characteristic polynomial of A, then 2 is an eigenvalue of A. (e) In order for an n x n matrix A to be diagonalizable, A must has n distinct eigenvalues.
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