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Unformatted text preview: A and B are similar n n matrices, then tr( A ) = tr( B ) and det( A ) = det( B ). 3. Let M,N be n n matrices and suppose that M is invertible. Denote A = MN and B = NM . Prove that A is similar to B . 4. Let A and B be invertible n n matrices. Prove that AB and BA have the same eigenvalues. 5. Determine if the following pair of matrices are similar to each other: A = 1 1 5 2 2 , B = 1 7 2 7 2 . 1...
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 Winter '08
 CELMIN
 Linear Algebra, Algebra, Eigenvectors, Vectors

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