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Let A and B be 6 by 6 matrices. Select all true statements below. A. If A and B have precisely the same eigenvalues counting multiplicity, then A is similar to B. B. If A is similar to B, then A and B have precisely the same eigenvalues counting multiplicity. C. The matrix A has 6 distinct eigenvalues. D. The matrix A has 6 real eigenvalues, counting multiplicity. E. If A is row equivalent to B, then A and B must have the same eigenvalues counting multiplicity. F. The matrix A has 6 eigenvalues, which may be complex numbers, counting multiplicity. G. None of the above

Let A and B be 6 by 6 matrices. Select all true statements below. A. If A and B have precisely the same eigenvalues counting multiplicity, then A is similar to B. B. If A is similar to B, then A and B have precisely the same eigenvalues counting multiplicity. C. The matrix A has 6 distinct eigenvalues. D. The matrix A has 6 real eigenvalues, counting multiplicity. E. If A is row equivalent to B, then A and B must have the same eigenvalues counting multiplicity. F. The matrix A has 6 eigenvalues, which may be complex numbers, counting multiplicity. G. None of the above

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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Let A and B be 6 by 6 matrices. Select all true statements below. A. If A and B have precisely the same eigenvalues counting multiplicity, then A is similar to B. B. If A is similar to B, then A and B have precisely the same eigenvalues counting multiplicity. C. The matrix A has 6 distinct eigenvalues. D. The matrix A has 6 real eigenvalues, counting multiplicity. E. If A is row equivalent to B, then A and B must have the same eigenvalues counting multiplicity. F. The matrix A has 6 eigenvalues, which may be complex numbers, counting multiplicity. G. None of the above
Transcribed Image Text:Let A and B be 6 by 6 matrices. Select all true statements below. A. If A and B have precisely the same eigenvalues counting multiplicity, then A is similar to B. B. If A is similar to B, then A and B have precisely the same eigenvalues counting multiplicity. C. The matrix A has 6 distinct eigenvalues. D. The matrix A has 6 real eigenvalues, counting multiplicity. E. If A is row equivalent to B, then A and B must have the same eigenvalues counting multiplicity. F. The matrix A has 6 eigenvalues, which may be complex numbers, counting multiplicity. G. None of the above
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