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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 Q-1 AQ = D for each of the following matrices A M n n ( F ), (a) A = -2 1 3 for F = R . (Solution) Q = -2-1 1 1 , D = 1 2 (b) A = i 1 2-i for F = C . (Solution) Q = 1 1 1-i-1-i , D = 1-1 (c) A = 3 1 1 2 4 2-1-1 1 for F = R . 1 (Solution) Q = 1 1 1 2-1-1-1 , D = 2 2 4 [Hint] i Determine all the eigenvalues of A . ii For each eigenvalue of A , nd the set of eigenvectors corre-sponding 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 Q-1 AQ = D . 2...
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