Question 1. Suppose GL(2, R) = {[a b] a, b, c, d € R, and ad — bc ± 0} be the 1 general linear group of 2 × 2 matrices over R under the matrix multiplication and SL(2, R) = {[a b]|a, b, c, d € R, and ad — bc = 1} be the special linear group of 2 x 2 matrices over R under the matrix multiplication. 1. Given an example of an element in GL(2, R) that is not in SL(2, R) 2. What is the inverse of [73] € SL(2, R)? 3. Explain why SL(2, R) is a subgroup of GL(2, R)
Question 1. Suppose GL(2, R) = {[a b] a, b, c, d € R, and ad — bc ± 0} be the 1 general linear group of 2 × 2 matrices over R under the matrix multiplication and SL(2, R) = {[a b]|a, b, c, d € R, and ad — bc = 1} be the special linear group of 2 x 2 matrices over R under the matrix multiplication. 1. Given an example of an element in GL(2, R) that is not in SL(2, R) 2. What is the inverse of [73] € SL(2, R)? 3. Explain why SL(2, R) is a subgroup of GL(2, R)
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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![Question 1. Suppose GL(2, R) = {[a b]|a, b, c, d € R, and ad — bc # 0} be the
—
-
general linear group of 2 × 2 matrices over R under the matrix multiplication and
SL (2, R) = {[a b] a, b, c, d € R, and ad — bc = 1} be the special linear group of
-
2 × 2 matrices over R under the matrix multiplication.
1. Given an example of an element in GL(2, R) that is not in SL(2, R)
2. What is the inverse of
[7 31
[2³] € SL (2, R)?
3. Explain why SL(2, R) is a subgroup of GL(2, R)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe00cebfb-aec4-474d-8979-79a2d105b819%2F60a480b1-aee0-4b3a-9bb3-76043c0135da%2F5wkkn6w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 1. Suppose GL(2, R) = {[a b]|a, b, c, d € R, and ad — bc # 0} be the
—
-
general linear group of 2 × 2 matrices over R under the matrix multiplication and
SL (2, R) = {[a b] a, b, c, d € R, and ad — bc = 1} be the special linear group of
-
2 × 2 matrices over R under the matrix multiplication.
1. Given an example of an element in GL(2, R) that is not in SL(2, R)
2. What is the inverse of
[7 31
[2³] € SL (2, R)?
3. Explain why SL(2, R) is a subgroup of GL(2, R)
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