(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Finding the fundamental matrix where psi(0) = the identity matrix

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