4. (i) Write the following permutations in S9 as a product of disjoint cycles 6 1 2 3 4 5 6 7 8 9 7 298 3 4 1 65 1 2 3 4 5 56 7 8 9 1 f = g= 7 89 2 3 4 (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 f, and compute f20 as a product of disjoint cycles. (v) Determine which of f, g and fg are even or odd.
4. (i) Write the following permutations in S9 as a product of disjoint cycles 6 1 2 3 4 5 6 7 8 9 7 298 3 4 1 65 1 2 3 4 5 56 7 8 9 1 f = g= 7 89 2 3 4 (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 f, and compute f20 as a product of disjoint cycles. (v) Determine which of f, g and fg are even or odd.
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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Transcribed Image Text:4.
(i) Write the following permutations in S9 as a product of disjoint cycles
6
1 2 3 4 5 6 7 8 9
7 29 8 3 4 1 6 5
1 2 3 4
5 6 7 8
5
9 1
f =
, 9 =
7 8 9
2 3 4
(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 f, and compute f20 as a product of disjoint cycles.
(v) Determine which of f, g and fg are even or odd.
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