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please do question 9 pleaase

please do question 9 pleaase

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please do question 9 pleaase

QUESTION 8 Consider the following 3 permutations in Sio σ= 1 2 3 4 5 6 7 8 9 10 1 4 5 6 8 10 79 23 - (₁ fl= 1 T= 12 3 4 5 6 7 8 9 10 2 5 10 4 9 7 6 38 1 2 3 4 5 6 7 8 9 10 10 9 8 4 3 2 1 5 6 7 (8.1) Compute rμ-¹0. (8.2) Express as a product of disjoint cycles and then as a product of transpositions. (8.3) Find the smallest value of n so that " = i, where i is the identity permutation. (8.4) Find ¹00 QUESTION 9 (9.1) Show that 3 € Z₁5 is a zero divisor. (9.2) Prove that in any ring R, if a € R is a zero divisor then it cannot be a unit. (9.3) Show that 2 is a unit in Z₁5 by finding its inverse. (9.3) Is Z₁5 a field? Explain. (9.4) When will Z, be a field?
Transcribed Image Text:QUESTION 8 Consider the following 3 permutations in Sio σ= 1 2 3 4 5 6 7 8 9 10 1 4 5 6 8 10 79 23 - (₁ fl= 1 T= 12 3 4 5 6 7 8 9 10 2 5 10 4 9 7 6 38 1 2 3 4 5 6 7 8 9 10 10 9 8 4 3 2 1 5 6 7 (8.1) Compute rμ-¹0. (8.2) Express as a product of disjoint cycles and then as a product of transpositions. (8.3) Find the smallest value of n so that " = i, where i is the identity permutation. (8.4) Find ¹00 QUESTION 9 (9.1) Show that 3 € Z₁5 is a zero divisor. (9.2) Prove that in any ring R, if a € R is a zero divisor then it cannot be a unit. (9.3) Show that 2 is a unit in Z₁5 by finding its inverse. (9.3) Is Z₁5 a field? Explain. (9.4) When will Z, be a field?
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