2010 Fall Quiz 2 - 4 Prove that if A and B are similar matrices then A is invertible if and only if B is invertible 5 Let A,B be n × n orthogonal

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QUIZ # 2–MATH349 Last Name: First Name: 1. Find bases for W and W R 3 , where W = x y z : x + y - 2 z = 0 . 2. If x is an eigenvector of A with eigenvalue λ = 3, show that x is also an eigenvector of A 2 - 5 A +3 I . What is the corresponding eigenvalue ? 3. Let A be a square matrix such that that A 3 = A . Show that λ = - 1 = 0 and λ = 1 are the only possible eigenvalues.
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Unformatted text preview: 4 Prove that if A and B are similar matrices, then A is invertible if and only if B is invertible. 5 Let A,B be n × n orthogonal matrices. Show that A ( A T + B T ) B = A + B and use the identity to prove that if det( A ) + det( B ) = 0, then A + B is not invertible....
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This note was uploaded on 02/20/2011 for the course MATH 302 taught by Professor Staff during the Fall '08 term at University of Delaware.

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