Consider the following 3 permutations in S10:σ=1 2 3 4 561 4 5 6 8 10789 107 9 2 3μl =T =12 32 5 1012 3 4 5 6 7 8 9 1010 9 8 4 3 2 1 5 674 54 96 7 8 9 103 8761Jompute τμ-1σ.Express μ as a product of disjoint cycles and then as a product of transpositions.Find the smallest value of n so that " = i, where i is the identity permutation.Find ¹00

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Answered: Consider the following 3 permutations…

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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Let A = 1. if ATX B = m = -2 -1 m n 1 -5 n = 3 0 and B= 1 -2 6 -2 5 -35 14 - 12 find mand ni (BTA)? 2. Is it possible to multiply BT by A (BTXA)?
Please do Exercise 14.4.21 part B and D. Please show step by step
Question 11 Let gcd(66,255) =d and there exist r,s € Z such that 255r+66s=d. Pick the correct value of r,s and d. Or= -7, s27 and d = 3 Or 7, s= 27 and d = 3 O r = 7, s= -27 and d = 3 Or=-7, s= -27 and d = 3 Question 12 Compute 139112 mod 27. (Use Euler theorem) 11 O 12 13 4 Question 13 Find the inverse of 49 modulo 53 O 11 12 O 13 10 O 14 11.
Obtain the generating function for the number of k-part compositions of n in which the ith part does not exceed 5i for all i = 1, 2, ... , k.
Compute the indicated products involving the following permutations of S, : 1 2 3 4 5 2 35 4 1 1 2 3 4 5 o = T = 3 54 1 2 (а) то (b) 7°o (c) o-l7 (d) o-27 (Note: µ-" = ()" for any natural number n and any permutation
2 3 4 5)(1 2 3 4 F. Consider the permutation (2 3 4 1 5)(1 3 5 4 2/ 1. Express as a product of disjoint cycles. 2. What is the order of the given permutation? 3. Express your answer in number 1 as a product of transpositions. 4. Determine whether the permutation is even or odd
I. Consider the permutation (1 2 3)(4 5)(1 2 5 4) ~². 1. Express as a product of disjoint cycles. 2. What is the order of the given permutation? 3. Express your answer in number 1 as a product of transpositions. 4. Determine whether the permutation is even or odd.
excercise 4.1 #2
Use the following examples to illustrate that if o and 7 are disjoint cycles then they commute. Otherwise, they do not commute. (a) In S3, let o = (1 2) and 7 = (2 3). (b) In S7, let o = (1 4 3) and 7 = (2 5 6).
excercise 4.1 #4
The cofactor C.;; of the entry a¡¡ is given by (-1)³ + İM¡¡. Substitute this expression in the cofactor expansion. Cij 87-6 1 -2 0 7 0 6 7 8 5 0 6 -3 -6 = 87-6 1 -20 7 0 6 7 8 5 0 6 -3 -6 1M 21 |(−1)² + ¹M ₂1 = + + |(−1)² + 2M 22- 7 -6 1 (-1) 7 8 5 6 -3 -6 (−1)² + ³M 23 The minor M,; of the entry a¡;; is the determinant of the matrix obtained by deleting the ith row and jth column. Use this fact to write the minors in the expansion. Remember that an even power of -1 is ij 1 and an odd power of -1 is -1. + + 87 1 (-1) 6 7 5 06-6 (-1)² + AM 24

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