The only root is the hence the in order to obtain a

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Unformatted text preview: ————————————————————————— CHAPTER 7. —— , resulting in , , . The corresponding solution is x The initial conditions x e , we solve the equations , resulting in , , . The corresponding solution is x The initial conditions x e , we solve the equations , resulting in , , . The corresponding solution is x Therefore the fundamental matrix is 12. The solution of the initial value problem is given by ________________________________________________________________________ page 407 —————————————————————————— CHAPTER 7. —— x x 13. Let It follows that is a scalar matrix, which is invertible, since the solutions are linearly independent. Let . Then The -th column of the product matrix is x, which is a solution vector, since it is a linear combination of solutions. Furthermore, the columns are all linearly independent, since the vectors x are Hence the product is a fundamental matrix. Finally, setting , I . This is precisely the definition of . 14....
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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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