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Homework Help: Basic Theory of Systems of First Order Linear Equations

  1. Apr 8, 2010 #1
    1. The problem statement, all variables and given/known data

    [I'm going to write column vectors as the row vectors transposed, since I don't have a fancy-schmancy equation-writing program]

    Consider the vectors x(1)(t)=(t 1)T and x(2)(t)=(t2 2t)T

    (a) Compute the Wronskian of x(1) and x(2).
    (b) In what intervals are x(1) and x(2) linearly independent?
    (c) What conclusion can be drawn about the coefficients in the system of homogenous differential equations satisfied by x(1) and x(2)?
    (d) Find this system of equations and verify the conclusions of part (c)?

    2. Relevant equations



    3. The attempt at a solution

    (a) are (b) are easy. The Wronskian it t2, and since vectors are only linearly independent if the determinant ≠ 0, the interval in this case is t≠0.

    Parts (c) and (d) have me stuck. Can you lead me in the right direction?
     
  2. jcsd
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