5. Let p be a prime number and let Fp denote the field with p elements,Fp = {0, 1,...,p-1}, equipped with the operations of arithmetic modulop. Consider the action of SL2 (Fp) on F2 defined by TA(V) := Av. Showthat the orbit of the vector (1) is the set of all nonzero vectors in F2. Howmany elements belong to the orbit and stabiliser of this vector? Use theseanswers to calculate |SL2(Fp)|.

5. Let p be a prime number and let denote the field with p elements, , equipped with the operations…

5. Let p be a prime number and let Fp denote the field with p elements, Fp = {0, 1,..., p-1}, equipped with the operations of arithmetic modulo p. Consider the action of SL2 (Fp) on F2 defined by A(V) := Av. Show that the orbit of the vector (1) is the set of all nonzero vectors in F2. How many elements belong to the orbit and stabiliser of this vector? Use these answers to calculate |SL2(Fp)|.

5. Let p be a prime number and let Fp denote the field with p elements, Fp = {0, 1,..., p-1}, equipped with the operations of arithmetic modulo p. Consider the action of SL2 (Fp) on F2 defined by A(V) := Av. Show that the orbit of the vector (1) is the set of all nonzero vectors in F2. How many elements belong to the orbit and stabiliser of this vector? Use these answers to calculate |SL2(Fp)|.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 5CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...

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