# Explicit Permutations, Transformations, Images and Kernels

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

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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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