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

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.2: Linear Independence, Basis, And Dimension

Problem 3AEXP

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