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Quiz+19+solution

Quiz+19+solution - MATH 17100 28446 Quiz 19 solution 11/30...

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MATH 17100 28446 Quiz 19 solution 11/30/ 2009 1. For the matrix 3 1 4 0 2 6 0 0 5 = A , find (i) The eigenvalues (ii) The corresponding eigenvectors Characteristic equation, 3 1 4 det( ) det 0 2 6 (3 )(2 )(5 ) 0 0 0 5 λ λ λ λ λ λ λ = = = A I 3, 2, 5 λ = For (1) 1 3, suppose corresponding eigenvector is λ = v 3 3 1 4 0 1 4 0 1 0 0 2 3 6 0 1 6 0 0 1 0 0 5 3 0 0 2 0 0 0 (1) (1) 2 3 and v v are basic variables and (1) 1 v is a free variable (1) 1 , arbitrary v α α = (1) (1) 2 3 0 and 0 v v = (1) 1 (1) (1) 2 (1) 3 1 0 0 0 0 v v v α α     = = =       v For (2) 2 2, suppose corresponding eigenvector is λ = v 3 2 1 4 1 1 4 1 1 0 0 2 2 6 0 0 6 0 0 1 0 0 5 2 0 0 3 0 0 0

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Quiz+19+solution - MATH 17100 28446 Quiz 19 solution 11/30...

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