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b. Which of the following statements are true? Select all that apply. OA. The matrices A and AT have the same eigenvalues, counting multiplicities. OB. The sum of two eigenvectors of a matrix A is also an eigenvector of A. OC. Each eigenvalue of A is also an eigenvalue of A?. OD. Each eigenvector of A is also an eigenvector of A?. DE. Each eigenvector of an invertible matrix A is also an eigenvector of A 1. c. Which of the following statements are true? Select all that apply. OA. Eigenvalues must be nonzero scalars. B. Eigenvectors must be nonzero vectors. | C. Two eigenvectors corresponding to the same eigenvalue are always linearly dependent. | D. A nonzero vector cannot correspond to two different eigenvalues of A.

b. Which of the following statements are true? Select all that apply. OA. The matrices A and AT have the same eigenvalues, counting multiplicities. OB. The sum of two eigenvectors of a matrix A is also an eigenvector of A. OC. Each eigenvalue of A is also an eigenvalue of A?. OD. Each eigenvector of A is also an eigenvector of A?. DE. Each eigenvector of an invertible matrix A is also an eigenvector of A 1. c. Which of the following statements are true? Select all that apply. OA. Eigenvalues must be nonzero scalars. B. Eigenvectors must be nonzero vectors. | C. Two eigenvectors corresponding to the same eigenvalue are always linearly dependent. | D. A nonzero vector cannot correspond to two different eigenvalues of A.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section: Chapter Questions
Problem 1RQ
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b. Which of the following statements are true? Select all that apply. ] A. The matrices A and AT have the same eigenvalues, counting multiplicities. B. The sum of two eigenvectors of a matrix A is also an eigenvector of A. C. Each eigenvalue of A is also an eigenvalue of A?. D. Each eigenvector of A is also an eigenvector of A?. ] E. Each eigenvector of an invertible matrixA is also an eigenvector of A 1. c. Which of the following statements are true? Select all that apply. A. Eigenvalues must be nonzero scalars. B. Eigenvectors must be nonzero vectors. c. Two eigenvectors corresponding to the same eigenvalue are always linearly dependent. D. A nonzero vector cannot correspond to two different eigenvalues of A.
Transcribed Image Text:b. Which of the following statements are true? Select all that apply. ] A. The matrices A and AT have the same eigenvalues, counting multiplicities. B. The sum of two eigenvectors of a matrix A is also an eigenvector of A. C. Each eigenvalue of A is also an eigenvalue of A?. D. Each eigenvector of A is also an eigenvector of A?. ] E. Each eigenvector of an invertible matrixA is also an eigenvector of A 1. c. Which of the following statements are true? Select all that apply. A. Eigenvalues must be nonzero scalars. B. Eigenvectors must be nonzero vectors. c. Two eigenvectors corresponding to the same eigenvalue are always linearly dependent. D. A nonzero vector cannot correspond to two different eigenvalues of A.
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