s11_mthsc853_hw08

S11_mthsc853_hw08 - MthSc 853(Linear Algebra Dr Macauley HW 8 Due Wednesday March 16th 2011(1 Consider the following matrices A = 2 2 B = 2 2 C = 3

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Unformatted text preview: MthSc 853 (Linear Algebra) Dr. Macauley HW 8 Due Wednesday, March 16th, 2011 (1) Consider the following matrices: A =- 2- 2 , B =- 2- 2 , C = 3 1- 1 1 . (a) Determine the characteristic and minimal polynomials of A , B , and C . (b) Determine the eigenvectors and generalized eigenvectors of A , B , and C . (2) Consider the following matrices: A = 2- 2 14 3- 7 2 , B = - 4 85 1 4- 30 3 , C = 2 2 1 0 2- 1 0 0 3 . A straightforward calculation shows that the characteristic polynomials are p A ( t ) = p B ( t ) = p C ( t ) = ( t- 2) 2 ( t- 3) . (a) Determine the minimal polynomials m A ( t ), m B ( t ), and m C ( t ). (b) Determine the eigenvectors and generalized eigenvectors of A , B , and C . (c) Determine which of these matrices are similar. (3) Compute the Jordan canonical form of the following matrices: A = - 1 0 1 2 1 2 1- 1 0 4- 6 1 , B = 1 0 0 1 2 1 0- 4 1 0 1- 2 0 0 0 1 ....
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This note was uploaded on 03/11/2012 for the course MTHSC 853 taught by Professor Staff during the Spring '08 term at Clemson.

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S11_mthsc853_hw08 - MthSc 853(Linear Algebra Dr Macauley HW 8 Due Wednesday March 16th 2011(1 Consider the following matrices A = 2 2 B = 2 2 C = 3

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