(please solve all parts) Let f be the homomorphism f: Z15 GL(2) of groups such that (1) = 4, where A- .a) Give the definition of f.b) Find K = Ker(/) and Zis / K.c) Find Im() and the bijective correspondence between Z/K and Im().

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Answered: Let f be the homomorphism f Z15 GL(2)…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 32E

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Let f be the homomorphism f Z15 GL(2) of groups such that (1)-A, where A- a) Give the definition of f. b) Find K- Ker() and Zis /K. ) Find Im() and the bijective correspondence between Z/K and Im().