The roots are real provided that first note that the

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Unformatted text preview: nd Hence one of the complex-valued solutions is given by ________________________________________________________________________ page 384 —————————————————————————— CHAPTER 7. —— x The general solution is x 6. Solution of the ODEs is based on the analysis of the algebraic equations . For a nonzero solution, we require that A I . The roots of the characteristic equation are . Setting , the two equations reduce to . The corresponding eigenvector is Hence one of the complex-valued solutions is given by x The general solution is ________________________________________________________________________ page 385 —————————————————————————— CHAPTER 7. —— x 8. The eigensystem is obtained from analysis of the equation . The characteristic equation of the coefficient matrix is roots , and equations reduce to The corresponding eigenvector is system of equations is equivalent to An eigenvector is given by , with , the . Setting With , the He...
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