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Can someone understand this passage of Linear Algebra?

  1. Nov 13, 2014 #1
    1. The problem statement, all variables and given/known data
    Hello there everybody! I'm reading a Linear Algebra textbook, specifically on LTV systems solutions.
    I'm trying to redo this example from the book:

    upload_2014-11-13_20-12-2.png

    2. Relevant equations

    But I couldn't understand the passage:

    upload_2014-11-13_20-12-26.png

    3. The attempt at a solution

    I mean. x1(0) = 1 and x2(0) = 0? I dont know from where that came from. And then x(t) = [1 0.5t^2]^T ?

    I can see from the x1(t) = x1(0) and x2(t) = (1/2)(t^2)x1(0) + x2(0) that

    x(t) = [1 0.5t^2]^T [x1(0) x2(0)] <= This I can relate!

    But the second one where x(t) = [ 1 2 ]^T I cant understand.

    I think it might have been arbitrarily choosen values? Either that or I'm missing some basic concept here. I've tried to get back some pages/chapters but could find the answer for that. Should I study the first chapters all again? (yeah probably I should! =/ )

    Anyway, could someone help me to understand this?

    Thank you very much!
     
    Last edited: Nov 13, 2014
  2. jcsd
  3. Nov 13, 2014 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I think you are correct that [1,0]^T and [1,2]^T are arbitrarily chosen linearly independent initial conditions. They didn't 'derive' them.
     
    Last edited: Nov 13, 2014
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