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hw6-solutions

# hw6-solutions - Assignment 6 More on Eigenvalues and...

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Assignment 6: More on Eigenvalues and Eigenvectors Written by: Saber Mirzaei Problem 1. (a) Since and are eigenvectors of then we have ( ) and ( ) hence: (b)

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Problem 2. (a) Using ( ) in Matlab/Octave we get the eigenvalues are and . a. For eigenvalue : ( ) [ ] Using rref: [ ] [ ] { [ ] [ ] [ ] , is a free variable so the vector [ ] is a base for eigenspace corresponding to eigenvalue . b. Using the same approach we get [ ] [ ] is the basis for eigenspace corresponding to eigenvalue . c. Using the same approach we get [ ] [ ] is the basis for eigenspace corresponding to eigenvalue .
(b) Using ( ) in Matlab/Octave we get the eigenvalues are and . a. Using the same approach as previous part we get [ ] [ ] is basis for eigenspace corresponding to eigenvalue . b. [ ] [ ] is basis for eigenspace corresponding to eigenvalue .

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Problem 3. (a) Another solution: ( ) (b) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Problem 4. (a) Since A is diagonalizable then: s.t. is diagonal and ( ) ( ) since the inverse of a diagonal matrix
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hw6-solutions - Assignment 6 More on Eigenvalues and...

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