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
icon
Related questions
Question
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.
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.
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,