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    Explicit Permutations, Transformations, Images and Kernels

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    Please do questions 2 and 6. Please see attached file.

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    https://brainmass.com/math/combinatorics/explicit-permutations-transformations-images-kernels-151703

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    Problem #2
    Proof:
    We know, for a cycle and any permutation , we have
    .
    Since , then
    , , , ,
    Therefore, we get

    Problem #6
    Proof:
    Since is a linear operator on a finite dimensional vector space , then is a module homomorphism. We have . Moreover, we have

    (a) First, I ...

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