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    Eigen function and eigenvalues

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    I have attached a problem involving eigenfunctions and eigenvalues. I would sure appreciate a complete explanation with work.

    Consider a linear operator ... with two sets of eigenfunctions and eigenvalues:
    ...
    with ... Now consider a linear combination of eigenfunctions, ... . Show whether or not ... is an eigenfunction of ...

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    https://brainmass.com/math/linear-algebra/eigen-function-eigenvalues-453208

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    The expert examines Eigen functions and eigenvalues.

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