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    Initial Value Problem, Ordinary Differential Equation: Jordan and Diagonalization

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    Find the solution of the system X' using the "diagonalization" technique (actually the Jordan form in this case)
    Please see the attached file.

    © BrainMass Inc. brainmass.com November 29, 2021, 11:53 pm ad1c9bdddf
    https://brainmass.com/math/ordinary-differential-equations/initial-value-problem-ordinary-differential-equation-jordan-diagonalization-8096

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    because,
    X' = AX + g
    A = = {(a11,a12,a13),(a21,a22,a23),(a31,a32,a33)}
    => A = {(2,0,0),(-1,0,-1),(1,1,2)}
    Now,
    (A - lI)X = 0
    => determinant (A-lI) = 0
    => l = 1,1,2 (= eigen values) => non diagonalizable
    => eigen vectors = (0,1,-1) for l =1, (1,-1,1) for l = 2 but for ...

    Solution Summary

    The solution to a system expressed as matrices is found. Initial value problems and ordinary differential equations are solved by using Jordan and Diagonalization.

    $2.49

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