This preview shows page 1. Sign up to view the full content.
Unformatted text preview: We have Ax = x . (a) A 2 x = A ( Ax ) = A ( x ) = Ax = 2 x . (b) Ax = x multiply both sides by A1 to get A1 Ax = A1 ( x ) or, equivalently, x = A1 x . Hence, 1 x = A1 x . (c) ( A + I ) x = Ax + Ix = x + x = ( + 1) x . 5. Problem Set 6.2, p. 298, # 4 A = S1 S . Here is the eigenvalue matrix and S is the eigenvector matrix of A . We have A + 2 I = S S1 + 2 SS1 = S ( + 2 I ) S1 . So the eigenvector matrix of A + 2 I is S and the eigenvalue matrix is + 2 I . 1...
View Full
Document
 Fall '11
 AnargyrosPapageorgiou

Click to edit the document details