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Please do Exercise 14.3.17 part A,C,E and please show step by step and explain

Please do Exercise 14.3.17 part A,C,E and please show step by step and explain

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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Please do Exercise 14.3.17 part A,C,E and please show step by step and explain

Example 14.3.16. At the beginning it may be helpful to draw a picture, as in the previous example. However, once you gain experience, you should be able to find the product of cycles directly. Consider the product or where a = (AEDBF) and 7 = (ABDFE). Then we have: • 1 takes A → B and o takes B →F; hence or takes A → F. • takes F → E, and o takes E → D; hence or takes F + D. • 1 takes D+ F, and o takes F + A; hence or takes D → A. We have finished a cycle: (AFD). Let us check where the other letters B,C, E go: T takes B → D, and o takes D - B; hence oT takes B + B. Neither 7 nor o affects C; hence or takes C -C. I takes E → A, and o takes A → E; hence or takes E → E. Since B, C, E are unaffected by or, we conclude that or = (AFD). Exercise 14.3.17. Given that ð = (135), a = (347), and p = (567) are permutations in S7, compute the following: (a) ốo (c) ốp (e) op (b) aổ (d) på (f) po
Transcribed Image Text:Example 14.3.16. At the beginning it may be helpful to draw a picture, as in the previous example. However, once you gain experience, you should be able to find the product of cycles directly. Consider the product or where a = (AEDBF) and 7 = (ABDFE). Then we have: • 1 takes A → B and o takes B →F; hence or takes A → F. • takes F → E, and o takes E → D; hence or takes F + D. • 1 takes D+ F, and o takes F + A; hence or takes D → A. We have finished a cycle: (AFD). Let us check where the other letters B,C, E go: T takes B → D, and o takes D - B; hence oT takes B + B. Neither 7 nor o affects C; hence or takes C -C. I takes E → A, and o takes A → E; hence or takes E → E. Since B, C, E are unaffected by or, we conclude that or = (AFD). Exercise 14.3.17. Given that ð = (135), a = (347), and p = (567) are permutations in S7, compute the following: (a) ốo (c) ốp (e) op (b) aổ (d) på (f) po
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