Explicit Permutations, Transformations, Images and Kernels
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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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