EGM4313.HW8

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

This preview shows pages 1–2. Sign up to view the full content.

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           

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online