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

  1. Dec 6, 2011 #1
    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?
     
  2. jcsd
  3. Dec 6, 2011 #2

    lanedance

    User Avatar
    Homework Helper

    just an idea but you have two linearly independent basis vectors call them u1, u2

    could you take a linear comibination of your vectors such that
    v1=au1+bu2 gives v1(0) = <1,0>
    and
    v2=cu1+du2 gives v2(0) = <0,1>?

    then could you use those basis vectors to write the reuired fundamental matrix?
     
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