Setting which corresponds to using in the modified

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Unformatted text preview: —— CHAPTER 7. —— For a nonzero solution, the determinant of the coefficient matrix must be zero. That is, Hence the eigenvalues are , yields and Substituting the first eigenvalue, The system is equivalent to the equation by x . A solution vector is given Substitution of results in , which reduces to 20. The eigenvalues . A corresponding solution vector is x and eigenvectors x satisfy the equation For a nonzero solution, we must have Hence the eigenvalues are eigenvector corresponding to , that is, and , set In order to determine the . The system of equations becomes , which reduces to Substitution of . A solution vector is given by x results in , which reduces to . A corresponding solution vector is x 22. The eigensystem is obtained from analysis of the equation ________________________________________________________________________ page 357 —————————————————————————— CHAPTER 7. —— . The characteristic equation of the coefficient matrix is roots , and . Setting , we have , with . This system is reduces to the equations A corresponding solution vector is given by x the reduced system of equations is S...
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This note was uploaded on 03/11/2014 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

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