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4. There is a theorem that says that every element g € GL(2, R) can be written, in a unique way, as kan for some k € K, a € A, and n € N (with K, A, N as in the last two problems). Your job: (a) If g = 0 (² 5 3-12 find k, a, n, such that g = kan.

4. There is a theorem that says that every element g € GL(2, R) can be written, in a unique way, as kan for some k € K, a € A, and n € N (with K, A, N as in the last two problems). Your job: (a) If g = 0 (² 5 3-12 find k, a, n, such that g = kan.

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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I NEED HELP WITH 4a not all problems just 4a please
2. Let G = GL(2, R). Prove that the following two subsets of GL(2, R) are subgroups of GL(2, R). (a) (b) 3. -{(82) = {(1₂1) : DER} A = N = Here's a trickier example of a subgroup of GL(2, R): 2)} ~ {( U If g = K = (² 3 If g = a> 0 and d> {(sir 0 5 - 12 -3 cos 3 sin 0 0} - sin cos Prove that K is indeed a subgroup of GL(2, R). (You will probably recognize the elements of K from an earlier homework.) cos o 4. There is a theorem that says that every element g = GL(2, R) can be written, in a unique way, as kan for some k € K, a € A, and n € N (with K, A, N as in the last two problems). Your job: (a) sin o sin o s)} - cos o (b) ( --77), find k, a, n, such that g = kan. For both of these, show your work and explain how you found your answers. Helpful fact: if det g > 0, then k will be a rotation, and if det g < 0, then k will be a reflection. find k, a, n, such that g = kan.
Transcribed Image Text:2. Let G = GL(2, R). Prove that the following two subsets of GL(2, R) are subgroups of GL(2, R). (a) (b) 3. -{(82) = {(1₂1) : DER} A = N = Here's a trickier example of a subgroup of GL(2, R): 2)} ~ {( U If g = K = (² 3 If g = a> 0 and d> {(sir 0 5 - 12 -3 cos 3 sin 0 0} - sin cos Prove that K is indeed a subgroup of GL(2, R). (You will probably recognize the elements of K from an earlier homework.) cos o 4. There is a theorem that says that every element g = GL(2, R) can be written, in a unique way, as kan for some k € K, a € A, and n € N (with K, A, N as in the last two problems). Your job: (a) sin o sin o s)} - cos o (b) ( --77), find k, a, n, such that g = kan. For both of these, show your work and explain how you found your answers. Helpful fact: if det g > 0, then k will be a rotation, and if det g < 0, then k will be a reflection. find k, a, n, such that g = kan.
Expert Solution
Step 1

Given:  g=053-12

          We have to find k, a, n such that g=kan where k∈K, a∈A and n∈N.

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