# The eigensystem is obtained from analysis of the

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Unformatted text preview: . For a nonzero solution, we must have A I is , which is an eigenvalue of multiplicity two. Setting coefficient matrix reduces the system to the single equation corresponding eigenvector is One solution is x . The only root is the . Hence the . In order to obtain a second linearly independent solution, we find a solution of the system . There equations reduce to . A second solution is . Set , some arbitrary constant. Then x Dropping the last term, the general solution is x ________________________________________________________________________ page 415 —————————————————————————— CHAPTER 7. —— 6. The eigensystem is obtained from analysis of the equation . The characteristic equation of the coefficient matrix is roots and . Setting , we have , with . This system is reduced to the equations A corresponding eigenvector vector is given by the system of equations is reduced to the single equation Setting , An eigenvector vector is given by Since the last equation has two free variables, a third linearly independent eigenvector associated with is Therefore the general s...
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