Math 235 Assignment 9 Due: Wednesday, Dec 1st 1. For any θ ∈ R , let R θ = ± cos θ-sin θ sin θ cos θ ² . a) Diagonalize R θ over C . b) Verify your answer in a) is correct, by showing the matrix P and diagonal matrix D from part a) satisfy P-1 R θ P = D for θ = 0 and θ = π 4 . 2. Let A = 0 2 1-2 3 0 1 0 2 . a) Given that λ = 2 + i is an eigenvalue of A , determine the other eigenvalues of A . b) Determine a real canonical form of A and give a change of basis matrix P that brings the matrix into this form. 3. Suppose that A is an n × n matrix with real entries, and that
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