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Deepak Patra posted an Question
October 31, 2021 • 11:42 am 30 points
  • IIT JAM
  • Mathematics (MA)

Q. 37 let v be a finite dimensional vector space and t:v-v be a linear transformation. let r(t) denote the range of t and n(t) denote the null space { v e v:tv

Q. 37 Let V be a finite dimensional vector space and T:V-V be a linear transformation. Let R(T) denote the range of T and N(T) denote the null space { v E V:Tv = 0} of T. If rank (T) = rank (T) then which of the following is/are necessarily True? (A)N(T) =N(T?). (B) R(T) =R(T?). C) N(T) nR(T) = {0}. (D)N(T) = {0}.

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