Finite Dimensional Vector Spaces IIT JAM Question | Mathematics CUET (PG) 2025 Question | Lec-8

[@iitjam_mathematics]

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[@hrishutiwari4929]

Sir next lecture mein ye explain kr dijiyega

[@Nainagour-l1h]

Sir homework ka answer option d is correct thank you sir radhe radhe 🙏

[@hrishutiwari4929]

Consider the action of S4 on Z [ x1,x2,x3,x4] given by σ.p(x1,x2,x3,x4) = p( xσ(1), xσ(2), xσ(3), xσ(4) ) for σ belongs to S4.Let H ⊆ S4 denote the cyclic subgroup generated by (1423). Then the cardinality of orbit OH(x1x3+x2x4) of H on the polynomial x1x3 + x2x4 is

[@Nainagour-l1h]

Since H is generated by (1423) the orbit x1x3+x2x4 under the action of H is the set {(1423)^n(x1x2+x2x4):n belong z}
Calculate the value of (1423)^4(x2x3+x2x4) for n=0,1,2,3,4
(1423)^0(x1x3+x2x4)=(x1x3+x2x4)
(1423)^1(" "")=(x4x1+x3x2)
(1423)^2( """)=(x2x4+x1x3)
(1423)^3( """")=(x3x2+x4x1)
(1423)^4( """)=(x1x3+x2x4)
The cardinality of the orbit oH (x1x3+x2x4) of H on the polynomial x1x3+x2x4 is 4
Answer 4

[@mansigupta9604]

D is the correct answer

[@hitendrakumar2070]

Option d will be the absolutely correct answer

[@hariomgupta9116]

H.W ka D correct hoga

[@as-bj4hq]

Option d correct

[@abhijitdas2976]

8:55 sir our question is G is not mentioned is abelian, cyclic, so kase HK is group

[@gauravkumaragnihotri6472]

Group was cyclic.

[@abhijitdas2976]

Option d