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Unformatted text preview: ———————————————————————— CHAPTER 7. ——
A corresponding solution vector is given by
, the reduced system of equations is Finally, setting A corresponding solution vector is given by
eigenvalues are distinct, the general solution is Since the x 15. Setting x results in the algebraic equations
. For a nonzero solution, we must have
A
I
. The roots of
the characteristic equation are
and
. With
, the system of equations
reduces to
. The corresponding eigenvector is
For the
case
, the system is equivalent to the equation
. An eigenvector is
Since the eigenvalues are distinct, the general solution is
x
Invoking the initial conditions, we obtain the system of equations Hence and , and the solution of the IVP is
x 17. Setting x results in the algebraic equations
. For a nonzero solution, we must have
roots of the characteristic equation are
we have A I
, and . Setting . The
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 Spring '08
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