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    Perturbed Linear System

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    Consider the perturbed linear system

    x' = (A + eB(t))x, x is an element of R^n,

    where A is a constant matrix, B is a bounded continuous matrix valued function, and e is a small parameter. Assume that all eigenvalues of A have non-zero real part.

    1) Show that the only bounded solution of the system is 0.

    2) If A has an eigenvalue with zero real part, then is the above still true?

    © BrainMass Inc. brainmass.com February 24, 2021, 2:27 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/perturbed-linear-system-21792

    Solution Summary

    This is a proof regarding the bounded solution of a perturbed linear system. The solution is enclosed within a Word document.

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