(i) Write the following permutations in S9 as a product of disjoint cycles 1 2 3 4 7 298 5 6 7 8 9 34 1 6 5 f = , 9 = 7 8 9 1 2 3 4 5 6 5 6 7 8 9 1 2 3 4 Calculate fg and write it both in two row notation and as a product of disjoint cycles. (iii) Calculate f-¹ and write it both in two row notation and as a product of disjoint cycles.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 42E
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(i) Write the following permutations in S9 as a product of disjoint cycles
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6
789
7 298 3 4 1 65
5 6 7 89 1 234
f
=
2
g=
=
(ii) Calculate fg and write it both in two row notation and as a product of disjoint cycles.
(iii) Calculate f-¹ and write it both in two row notation and as a product of disjoint cycles.
(iv) Find the order of ƒ, and compute ƒ2⁰ as a product of disjoint cycles.
(v) Determine which of f, g and fg are even or odd.
Transcribed Image Text:(i) Write the following permutations in S9 as a product of disjoint cycles 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 789 7 298 3 4 1 65 5 6 7 89 1 234 f = 2 g= = (ii) Calculate fg and write it both in two row notation and as a product of disjoint cycles. (iii) Calculate f-¹ and write it both in two row notation and as a product of disjoint cycles. (iv) Find the order of ƒ, and compute ƒ2⁰ as a product of disjoint cycles. (v) Determine which of f, g and fg are even or odd.
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