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If S is the change of variable transformation on Pn(x) defined by =S(P(x)) = P(x2) and T is the multiplication transformation on Pn(x) defined by

Then which of the followings is not true?
  • a)
    S and T are commute
  • b)
    Ker ST = ker TS
  • c)
    ST and TS both are one - one map
  • d)
    ST ≠ TS
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If S is the change of variable transformation on Pn(x) defined by =S(P...
(ST) P(x) = S(TP(x))
= S(x2P(x))
= x4 P(x2)
and (TS) P(x) = T (SP(x))
= T(P(x2))
= x2 P(x2)
⇒ ST ≠ TS
Now ker(ST) = 

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If S is the change of variable transformation on Pn(x) defined by =S(P(x)) = P(x2)and T is the multiplication transformation on Pn(x) defined byThen which of the followings is not true?a)S and T are commuteb)Ker ST = ker TSc)ST and TS both are one - one mapd)ST ≠ TSCorrect answer is option 'A'. Can you explain this answer?
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