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6. Let GL2(R) be the group of 2 × 2 invertible matrices, with multiplication. (The elements of GL2(R) have real entries and non-zero determinant.) Consider the matrix: A- (: :) 1 1 1

6. Let GL2(R) be the group of 2 × 2 invertible matrices, with multiplication. (The elements of GL2(R) have real entries and non-zero determinant.) Consider the matrix: A- (: :) 1 1 1

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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a) Find the cyclic subgroup H of GL2(R) generated by the matrix A: H = (A) = {A* : k e Z}. b) Find a familiar group isomorphic to H. Explicitly provide an isomorphism (and check that the given map is, indeed, an isomorphism).
Transcribed Image Text:a) Find the cyclic subgroup H of GL2(R) generated by the matrix A: H = (A) = {A* : k e Z}. b) Find a familiar group isomorphic to H. Explicitly provide an isomorphism (and check that the given map is, indeed, an isomorphism).
6. Let GL2(R) be the group of 2 × 2 invertible matrices, with multiplication. (The elements of GL2 (R) have real entries and non-zero determinant.) Consider the matrix: A-(; ;). 1
Transcribed Image Text:6. Let GL2(R) be the group of 2 × 2 invertible matrices, with multiplication. (The elements of GL2 (R) have real entries and non-zero determinant.) Consider the matrix: A-(; ;). 1
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