Unformatted text preview: m is equivalent to the equations Finally, upon setting , The corresponding eigenvector is Hence the general solution is x
Invoking the initial conditions, It follows that , and . Hence the solution of the IVP is x 19. Set x . Substitution into the system of differential equations results in
A which upon simplification yields is, A
must satisfy A
I
0
21. Setting x , 0 Hence the vector and constant results in the algebraic equations ________________________________________________________________________
page 373 —————————————————————————— CHAPTER 7. —— .
For a nonzero solution, we must have
A
I
the characteristic equation are
and
. With
reduces to
. The corresponding eigenvector is
case
, the system is equivalent to the equation
It follows that
x . The roots of
, the system of equations
For the
. An eigenvector is and x The Wronskian of this solution set is
xx
. Thus the solutions are linearly
independent for
. Hence the general solution is
x 22. As shown in Prob. , solution of the ODE requ...
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 Spring '08
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 Linear Algebra, eigenvector

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