2. Let G by the symmetric group S(n) and V the complex vectorspace with basis {v1, v2,..., Vn}. For T E G and any v =...+ A,vn of V, definedv1+T· V = A1V#(1) + · + \„V#(n)·MATH4409Show that V is a G-set and find both the orbit Gv and thestabilizer G, when(a) n = 4 and v= v1 + v2+ v3 + v4;(b) n = 4 and v = vị + v3

Answered: Image /qna-images/answer/1860af29-080e-4431-84e7-343d97cb7f21.jpg

2. Let G by the symmetric group S(n) and V the complex vector space with basis {v1, v2,..., vn}. For a E G and any v = 1vi+ + Anvn of V, define T. v = A1U#(1) ++ A,V#(n)- MATH440 9. Show that V is a G-set and find both the orbit Gv and the stabilizer G, when (a) n = 4 and v = v1 + v2+ v3 + v4; (b) n = 4 and v = v1 + V3

2. Let G by the symmetric group S(n) and V the complex vector space with basis {v1, v2,..., vn}. For a E G and any v = 1vi+ + Anvn of V, define T. v = A1U#(1) ++ A,V#(n)- MATH440 9. Show that V is a G-set and find both the orbit Gv and the stabilizer G, when (a) n = 4 and v = v1 + v2+ v3 + v4; (b) n = 4 and v = v1 + V3

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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