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(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.

(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.

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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(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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