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Math Help - vector differential equations

  1. #1
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    vector differential equations

    Determine the general solutions to the system x'=Ax for the given matrix A.
    A= -2, 0, 0
    1,-3,-1
    -1, 1,-1

    Please help me. I am stuck up in taking v0.
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  2. #2
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    Quote Originally Posted by priyanka View Post
    Determine the general solutions to the system x'=Ax for the given matrix A.
    A= -2, 0, 0
    1,-3,-1
    -1, 1,-1

    Please help me. I am stuck up in taking v0.
    Do you have anymore information? I.e x_0 ?
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  3. #3
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    The two linearly independent solutions can be constructed from the eigenvectors of the given matrix. The third linearly independent solution will be of the form x1(t) = e^(lamda(t))(v1 + tv0).

    can u help me now.
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  4. #4
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    Quote Originally Posted by priyanka View Post
    Determine the general solutions to the system x'=Ax for the given matrix A.
    A= -2, 0, 0
    1,-3,-1
    -1, 1,-1

    Please help me. I am stuck up in taking v0.
    The eigenvalue equation for A is \left|\begin{array}{ccc}-2-\lambda & 0 & 0 \\ 1 & -3-\lambda & -1 \\ -1 & 1 & -1-\lambda\end{array}\right|= 0. Solve that. Expanding by the first row should make that particularly easy. I don't know what you mean by "taking v0".
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