Show that each type of map from Example 1.8 is an automorphism. (a) Dilation ds by a
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(a) Dilation ds by a nonzero scalar s.
(b) Rotation tθ through an angle θ.
(c) Reflection fℓ over a line through the origin.
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a This map is onetoone because if ds 1 ds 2 then by definition of the map s 1 s 2 and so 1 2 as s is nonzero This map is onto as any 2 R 2 is the imag...View the full answer
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