EGM4313.HW8 - Problem 7, page 147: Find the eigenvalues of...

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Problem 7, page 147: Find the eigenvalues of the coefficient matrix. Note that the matrix is skew-symmetric so that the eigenvalues are either zero or pure imaginary. Since there are an odd number of them and they come in complex conjugate pairs we know that “0” must be one of the eigenvalues. 2 11 1 1 ( 1) 0 0, 2 01 i      Now find the eigenvectors: For 0 we have 1 0 1    and for 2 i we have 10 1 2 0 2 1 1 0 ii  The general solution is 1 2 3 00 1 1 1 0 0 cos( 2 ) 2 sin( 2 ) 2 cos( 2 ) 0 sin( 2 ) 1 1 0 0 1 C C t t C t t           Problem 9, page 147: The matrix 10 10 4 10 1 14 4 14 2 A   has eigenvalues 18,9,18  (details skipped) The eigenvectors are 1 2 2 2 , 1 , 2 2 2 1                          respectively, hence 18 9 18 1 2 3 1 2 2 2 1 2 2 2 1 t t t C e C e C e           
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EGM4313.HW8 - Problem 7, page 147: Find the eigenvalues of...

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