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2. Compute each of the following. (2bdm from 5.4) (2361)(CD) 10 (VCC1) (93)(VE) (EC) 19

2. Compute each of the following. (2bdm from 5.4) (2361)(CD) 10 (VCC1) (93)(VE) (EC) 19

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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### Topic: Computing Permutations #### Exercise 2: Compute Each of the Following (Based on 2bdm from Section 5.4) For this exercise, we will compute the following permutations: ##### a) \((12)(1253)\) ##### b) \((1423)(34)(56)(1324)\) ##### c) \((12)^{-1}\) To solve these problems, you will need to understand permutation notation and the concept of permutation composition and inverses. --- **Important Points to Note:** 1. **Permutation Notation**: - Permutations are denoted by cycles, for example, \((12)\) shifts the positions of 1 and 2. - The cycle \((1253)\) means that 1 is mapped to 2, 2 is mapped to 5, 5 is mapped to 3, and 3 is mapped back to 1. 2. **Composition of Permutations**: - To compose permutations, apply the rightmost permutation first. 3. **Inverse Permutation**: - The inverse of a permutation reverses the mapping of a cycle. For example, the inverse of \((12)\) is also \((12)\), as it simply swaps 1 and 2 again to return to the original position. By understanding these concepts, you can solve each part of the exercise methodically.
Transcribed Image Text:### Topic: Computing Permutations #### Exercise 2: Compute Each of the Following (Based on 2bdm from Section 5.4) For this exercise, we will compute the following permutations: ##### a) \((12)(1253)\) ##### b) \((1423)(34)(56)(1324)\) ##### c) \((12)^{-1}\) To solve these problems, you will need to understand permutation notation and the concept of permutation composition and inverses. --- **Important Points to Note:** 1. **Permutation Notation**: - Permutations are denoted by cycles, for example, \((12)\) shifts the positions of 1 and 2. - The cycle \((1253)\) means that 1 is mapped to 2, 2 is mapped to 5, 5 is mapped to 3, and 3 is mapped back to 1. 2. **Composition of Permutations**: - To compose permutations, apply the rightmost permutation first. 3. **Inverse Permutation**: - The inverse of a permutation reverses the mapping of a cycle. For example, the inverse of \((12)\) is also \((12)\), as it simply swaps 1 and 2 again to return to the original position. By understanding these concepts, you can solve each part of the exercise methodically.
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