This exercise provides an alternative to Theorem 8.2 for factoring an r-cycle into transpositions. Prove that (x1, X2, X3, ..., X,) =(x1, x2) • (x2, x3) • (x3, x4) • • • (x,2 Xr-1)• (X-1, *,). O ...O

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A: I haved proved using possible cases of order of Z(G)

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Q: IF possible. Hhe eigen values for Exercisedis) is as follow: 16 2 -2 -2

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A: I have proved using mathematical induction

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A: See the attachment

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