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    Eigenvectors

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    D and E are nxn matrices, E is invertible, DE = ED, and u is an eigenvector for D corresponding to x=5.

    a. Show that Eu is also an eigenvector for D corresponding to x=5.

    b. Show that u is an eigenvector for D^2.

    c. Show that u is an eigenvector for
    D^2 - 3D.

    © BrainMass Inc. brainmass.com March 4, 2021, 5:35 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/computing-proof-regarding-eigenvectors-matrices-1563

    Solution Preview

    See the attached file.
    a) We know:

    Du=5u (u is eigenvector for 5) and DE=ED(*). Let's multiply the first equality by E to the left.

    Then, EDu=5Eu so DEu=5Eu because of ...

    Solution Summary

    The solution provides a proof regarding eigenvectors and matrices.

    $2.19

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