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Given the set of matrices M = {I, A, B, C, D, K} where 1 -( :) 0 I = 0 1 --(: :) C = -1 1 +-(13) :) A = 0 -(:::) 1 D = --(:::) B = -1 0 *-(: :) a) Explain why (show that) M≤ GL₂(R) b) Does M have any generators? If so which elements of M generate the group? If not, is there a set of elements of M that generate the group? c) Determine the order of each element of M

Given the set of matrices M = {I, A, B, C, D, K} where 1 -( :) 0 I = 0 1 --(: :) C = -1 1 +-(13) :) A = 0 -(:::) 1 D = --(:::) B = -1 0 *-(: :) a) Explain why (show that) M≤ GL₂(R) b) Does M have any generators? If so which elements of M generate the group? If not, is there a set of elements of M that generate the group? c) Determine the order of each element of M

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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Given the set of matrices M = 1 0 --(68) I = 0 1 0-(41) C = {I, A, B, C, D, K} where 1 -1 ~-(:) A = 1 0 -1 0-(:4) D = 1 -1 B = -(::) -1 -1 *-( :) K = (a) Explain why (show that) M ≤ GL2(R) (b) Does M have any generators? If so which elements of M generate the group? If not, is there a set of elements of M that generate the group? c) Determine the order of each element of M
Transcribed Image Text:Given the set of matrices M = 1 0 --(68) I = 0 1 0-(41) C = {I, A, B, C, D, K} where 1 -1 ~-(:) A = 1 0 -1 0-(:4) D = 1 -1 B = -(::) -1 -1 *-( :) K = (a) Explain why (show that) M ≤ GL2(R) (b) Does M have any generators? If so which elements of M generate the group? If not, is there a set of elements of M that generate the group? c) Determine the order of each element of M
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