Unformatted text preview: We have Ax = Î»x . (a) A 2 x = A ( Ax ) = A ( Î»x ) = Î»Ax = Î» 2 x . (b) Ax = Î»x multiply both sides by A1 to get A1 Ax = A1 ( Î»x ) or, equivalently, x = Î»A1 x . Hence, Î»1 x = A1 x . (c) ( A + I ) x = Ax + Ix = Î»x + x = ( Î» + 1) x . 5. Problem Set 6.2, p. 298, # 4 A = S1 Î› S . Here Î› is the eigenvalue matrix and S is the eigenvector matrix of A . We have A + 2 I = S Î› S1 + 2 SS1 = S (Î› + 2 I ) S1 . So the eigenvector matrix of A + 2 I is S and the eigenvalue matrix is Î› + 2 I . 1...
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 Fall '11
 AnargyrosPapageorgiou
 Linear Algebra, Orthogonal matrix, Q1 Q2

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