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    Eigenvectors and eigenvalues

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    Please see the attached file for full problem description.
    ? Let . Compute the characteristic polynomial and all eigenvalues and all eigenvectors of A.

    ? True or false? Justify your answer in each case (giving a proof or a counterexample);

    Let be a linear transformation which is an isomorphism. Denote its inverse by . Suppose that is an eigenvalue of T. then

    b) is an eigenvalue of .
    c) - is an eigenvalue of
    d) is an eigenvalue of .

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    Solution Summary

    This shows how to compute the characteristic polynomial and all eigenvalues and all eigenvectors, and show that given values are the eigenvalues of an inverse transformation matrix.