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(Solved): Replace nz+ by n=8. Then what is the solution? 25. Let nZ+, let r and s be the usual generator ...



Replace n€z+ by n=8. Then what is the solution?
25. Let \( n \in \mathbb{Z}^{+} \), let \( r \) and \( s \) be the usual generators of \( D_{2 n} \) and let \( \theta=2 \pi
25. Let , let and be the usual generators of and let . (a) Prove that the matrix is the matrix of the linear transformation which rotates the plane about the origin in a counterclockwise direction by radians. (b) Prove that the map defined on generators by extends to a homomorphism of into . (c) Prove that the homomorphism in part (b) is injective.


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(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
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