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Unformatted text preview: V has a basis consisting of eigenvectors of T . (Solution) True. 2. Determine an invertible matrix Q and a diagonal matrix D such that Q1 AQ = D for each of the following matrices A M n n ( F ), (a) A = 2 1 3 for F = R . (Solution) Q = 21 1 1 , D = 1 2 (b) A = i 1 2i for F = C . (Solution) Q = 1 1 1i1i , D = 11 (c) A = 3 1 1 2 4 211 1 for F = R . 1 (Solution) Q = 1 1 1 2111 , D = 2 2 4 [Hint] i Determine all the eigenvalues of A . ii For each eigenvalue of A , nd the set of eigenvectors corresponding to . iii Find a basis for F n consisting of eigenvectors of A . iv Determine an invertible matrix Q and a diagonal matrix D such that Q1 AQ = D . 2...
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This note was uploaded on 10/02/2009 for the course MATH 54554 taught by Professor Holtz during the Spring '06 term at University of California, Berkeley.
 Spring '06
 Holtz
 Linear Algebra, Algebra

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