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Unformatted text preview: is worth 5 points. You do NOT need to justify your answers, and partial credit will NOT be given. a) True or false? The matrix p 5 4 i − 4 i − 1 P has orthogonal eigenvectors. b) True or false? The matrix 1 √ 7 p 2 − i − 1 + i 1 + i 2 + i P is unitary. c) Let x ( t ) be the solution to d x dt = A x , where A = 1 2 3 − 1 − 1 4 − 2 1 5 − 3 − 4 − 5 and x (0) = (5 , − 3 , 1 , 1) T Find the limit, as t → ∞ , of  x ( t )  . (This has a quick 1 and easy solution, and you do NOT have to diagonalize A !) d) True or false? If a matrix M satisFes M = M T , then the eigenvalues of M are real. e) True or false? If a matrix is unitary, then it is not Hermitian. 2...
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 Spring '08
 RAdin
 Linear Algebra, Algebra, inner product, Gram Schmidt, Compute Ag, usual inner product

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