please do question 9 pleaase
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 76E
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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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffae114b-415c-49a6-86f3-c4318b25373e%2F8b3a17be-bcfe-469f-b312-31a77dc1e2d7%2Futw85e4_processed.png&w=3840&q=75)
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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