X the coefficient matrix is symmetric hence the

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Unformatted text preview: ————————————————— CHAPTER 7. —— x , which is a constant vector. A second linearly independent solution is obtained from the system . The equations reduce to the single equation Let , and a second linearly independent solution is . We obtain x Dropping the last term, the general solution is x Imposing the initial conditions, we require that , which results in and Therefore the solution of the IVP is x ________________________________________________________________________ page 420 —————————————————————————— CHAPTER 7. —— 12. The characteristic equation of the system is . The eigenvalues are and . The eigenvector associated with is Setting , the components of the eigenvectors must satisfy the relation 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 solution may be written as x Invoki...
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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.

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