The system of equations becomes which reduces to

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Unformatted text preview: _______ page 355 —————————————————————————— CHAPTER 7. —— of the other. However, there is no nonzero scalar, , such that and for all . Therefore the vectors are linearly independent. 16. The eigenvalues and eigenvectors x satisfy the equation For a nonzero solution, we must have The eigenvalues are x are solutions of the system , that is, and The two equations reduce to , we have The components of the eigenvector . Hence x Now setting , with solution given by x 17. The eigenvalues and eigenvectors x satisfy the equation For a nonzero solution, we must have The eigenvalues are becomes and , that is, For , the system of equations , which reduces to Substituting . A solution vector is given by x , we have . The equations reduce to . Hence a solution vector is given by x 19. The eigensystem is obtained from analysis of the equation ________________________________________________________________________ page 356 ————————————————————————...
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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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