QUESTION 8 Consider the following 3 permutations in S10: o= 1 2 3 4 5 6 7 8 1 4 5 6 8 10 7 9 9 10 2 3 12 3 4 5 6 2 5 10 4 9 7 2 3 5 6 7 9 10 μ= -(₁ (10 3 8 4 3 2 1 8 8 7 ) 7 8 9 6 3 8 (8.1) Compute ru ¹0. (8.2) Express μ as a product of disjoint cycles and then as a product of transpositions. (8.3) Find the smallest value of n so that "=i, where i is the identity permutation. (8.4) Find 100 10 1 ( (

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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QUESTION 8
Consider the following 3 permutations in S10:
1 2 3 4 5 6 7 8 9 10
1 4 5 6 8 10 7 9 2 3
T=
1 2 3 4 5 6 7 8
10 4 9 7
2 5
6
3
1
2 3 4 5 6 7 8 9 10
(6 847)
μ=
9 10
8
1
(8.1) Compute rμ-¹0.
(8.2) Express μ as a product of disjoint cycles and then as a product of transpositions.
(8.3) Find the smallest value of n so that "=i, where i is the identity permutation.
(8.4) Find 100
Transcribed Image Text:QUESTION 8 Consider the following 3 permutations in S10: 1 2 3 4 5 6 7 8 9 10 1 4 5 6 8 10 7 9 2 3 T= 1 2 3 4 5 6 7 8 10 4 9 7 2 5 6 3 1 2 3 4 5 6 7 8 9 10 (6 847) μ= 9 10 8 1 (8.1) Compute rμ-¹0. (8.2) Express μ as a product of disjoint cycles and then as a product of transpositions. (8.3) Find the smallest value of n so that "=i, where i is the identity permutation. (8.4) Find 100
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