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# 12 the characteristic equation of the system is the

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Unformatted text preview: limit does exist. In fact, Ax Term-by-term differentiation results in ________________________________________________________________________ page 411 —————————————————————————— CHAPTER 7. —— I A AI A A A A A A A x x A x That is, A Furthermore, . x . Based on uniqueness of solutions, . ________________________________________________________________________ page 412 —————————————————————————— CHAPTER 7. —— Section 7.8 2. Setting x results in the algebraic equations . The characteristic equation is reduces the system of equations to One solution is , with the single root . Substituting . Therefore the only eigenvector is x , which is a constant vector. In order to generate a second linearly independent solution, we must search for a generalized eigenvector. This leads to the system of equations . This system also reduces to a single equation, . Setting arbitrary constant, we obtain . A second solution is , some x Note that the last term is a multiple of x x and may be dropped. Hence...
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