hw7-solutions

Step 5 and and and b

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Unformatted text preview: the same steps we get: [ Problem 5. (a) ̂ ( ) (b) Any vector in ( ) has the form , use exercise 28 since is symmetric: ( )( ) → for some . To show that → ̂ is orthogonal to [( [ ( ̂) ̂)] ̂ is in ( ). So , and the ̂( ̂) express as the sum of a vector in and a vector in decomposition . By the orthogonal decomposition theorem in section 6.3, this decomposition is unique, and so ̂ must be Problem 6. (a) For [ the eigenvalues are and . Corresponding eigenvectors will be the solutions for For [ For [ ] the nor...
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