3. Let GL2 (R) be the group of all 2 x 2 nonsingular matrices with entries in R, and let SL2(Z)be the subset of GL2(R) given bySL2(Z) = {A € GL2(R) | all entries of A are in Z and det(A) = 1}.%3D(a) Prove that SL2(Z) is a subgroup of GL2(R).(b)) Let n be a positive integer, and let H be the subset of SL2(Z) given by1+ npngH :A E SL2(Z) | A:for some p, q, r, s E Znr1+ nsProve that H is a normal subgroup of SL2(Z).

Answered: Image /qna-images/answer/af5a983b-9785-40aa-86e5-e0f1cf6874a0.jpg

3. Let GL2(R) be the group of all 2 x 2 nonsingular matrices with entries in R, and let SL2(Z) be the subset of GL2(R) given by SL2(Z) = {A € GL2(R) | all entries of A are in Z and det (A) = 1}. (a) Prove that SL2(Z) is a subgroup of GL2(R). (b)) Let n be a positive integer, and let H be the subset of SL2(Z) given by 1+ np ng A E SL2(Z) | A = = H for some p, q, r; nr 1+ ns

3. Let GL2(R) be the group of all 2 x 2 nonsingular matrices with entries in R, and let SL2(Z) be the subset of GL2(R) given by SL2(Z) = {A € GL2(R) | all entries of A are in Z and det (A) = 1}. (a) Prove that SL2(Z) is a subgroup of GL2(R). (b)) Let n be a positive integer, and let H be the subset of SL2(Z) given by 1+ np ng A E SL2(Z) | A = = H for some p, q, r; nr 1+ ns

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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