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Homework Help: Eigenvalues of coefficient matrix problem

  1. Mar 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine the general solution of the system of homogeneous differential equations.
    The system of homogeneous differential equations is:
    X'[itex]_{1}[/itex](t) = 141x[itex]_{1}[/itex](t) - 44x[itex]_{2}[/itex](t)
    X'[itex]_{2}[/itex](t) = 468x[itex]_{1}[/itex](t) - 146[itex]_{2}[/itex](t)

    What is Eigenvalues of Coefficient Matrix?
    What is corresponding eigenvectors?
    What is expression for x[itex]_{1}[/itex](t)?
    What is expression for x[itex]_{2}[/itex](t)
    2. Relevant equations

    3. The attempt at a solution
    What is Eigenvalues of Coefficient Matrix?
    |144 - 44 | = A
    |146 -146|
    det|144-λ -44 | = P(λ)
    |468 -146-λ|
    = (144-λ)(-146-λ) - (-44)(468)
    = -21024 -144λ +146λ + λ[itex]^{2}[/itex] + 20592
    = λ[itex]^{2}[/itex] +2λ -432
    Do I use quadratic equation to find λ?
  2. jcsd
  3. Mar 17, 2012 #2
    yes of course, then you find the eigenvectors, then you find your solution to the DE using these eigenvectors
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