Which of the following statements is/are true? (i) Any two eigenvectors of a matrix A are linearly independent. (ii) It is possible for a square matrix with real entries to have infinite number of eigenvect (iii) Every square matrix is diagonalizable. OA. Only (iii) OB. Only (ii) OC. All of the given statements. O D. None of the given statements. O E. Only (i)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 19AEXP
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Which of the following statements is/are true?
(i) Any two eigenvectors of a matrix A are linearly independent.
(ii) It is possible for a square matrix with real entries to have infinite number of eigenvectors.
(iii) Every square matrix is diagonalizable.
O A. Only (iii)
OB. Only (ii)
O C. All of the given statements.
O D. None of the given statements.
O E. Only (i)
Transcribed Image Text:Which of the following statements is/are true? (i) Any two eigenvectors of a matrix A are linearly independent. (ii) It is possible for a square matrix with real entries to have infinite number of eigenvectors. (iii) Every square matrix is diagonalizable. O A. Only (iii) OB. Only (ii) O C. All of the given statements. O D. None of the given statements. O E. Only (i)
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