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**1. The problem statement, all variables and given/known data**

If I have a solution to a system of first order linear equations: [itex]<x,y> = c_1 e^{-3t} <1,-1> + c_2 e^{-t} <1,1>[/itex] , how do I find the fundamental matrix psi(t) so that psi(0) = I ?

**2. Relevant equations**

**3. The attempt at a solution**

[itex]psi(t) = <<e^{3t}, e^{-t}>, <-e^{-3t}, e^{-t}>>[/itex]

[itex]psi(0) = <<1, 1>, <-1, 1>>[/itex]

This is clearly not the identity matrix.

Now what?