Unformatted text preview: are after the general solution x = c 1 u 1 + c 2 u 2 In chapter 2, where we considered a single variable, we had a solution x = ce rt This would suggest that we try the solution 5 x = e λ t v where λ is an unknown constant and v is an unknown vector of constants. If we do this and substitute into the differential equation system we have λ e λ t v = A e λ t v eliminating the term e λ t we have λ v = Av i.e. ( A − λ I ) v = For a nontrivial solution we require that det( A − λ I ) = 5 Here u = e rt v ....
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 Fall '11
 Dr.Gwartney
 Economics, Derivative, Vector Space, Elementary algebra, Economic Dynamics

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