Home /
Expert Answers /
Other Math /
replace-nz-by-n-8-then-what-is-the-solution-25-let-nz-let-r-and-s-be-the-usual-generator-pa177

Replace n€z+ by n=8. Then what is the solution?

25. Let $n?Z_{+}$, let $r$ and $s$ be the usual generators of $D_{2n}$ and let $?=2?/n$. (a) Prove that the matrix $(cos?sin???sin?cos??)$ is the matrix of the linear transformation which rotates the $x,y$ plane about the origin in a counterclockwise direction by $?$ radians. (b) Prove that the map $?:D_{2n}?GL_{2}(R)$ defined on generators by $?(r)=(cos?sin???sin?cos??)and?(s)=(01?10?)$ extends to a homomorphism of $D_{2n}$ into $GL_{2}(R)$. (c) Prove that the homomorphism $?$ in part (b) is injective.

(a) To prove that the matrix [cos???sin??sin??cos??] is the matrix of the linear transformation which rotates the x,y plane about the origin in a coun

Live Sessions

Online Lab Report Help

Online Project Report Help

Online Assignment Help

Essay Writing Help

CPM Homework Help

Mortgage Calculator

Electrical Engineering

Civil Engineering

Chemical Engineering

Electronics and Communication Engineering

Mathematics

Physics

Chemistry

Software Works/ Computer Science

Other Subjects

100% Correct Solutions

24/7 Availability

One stop destination for all subject

Cost Effective

Solved on Time

Plagiarism Free Solutions

Confidentiality