CSIR NET
Sonika Jain Asked a Question
September 23, 2020 7:24 pmpts 30 pts
  • CSIR NET
  • Mathematical Sciences

does rank nullity thrm always implies T is bijective?means evry linear trans. T is always bujective becz ds conditn of R-N thrm holds for evry Trans T

T(B) hence p(T) = 2 and n(T) = 1 implies T is neither one-one nor onto. 6. Let V be vector space, and let T: V>V be linear operator. If V is finite-dimensional, the nullity (T) + rank (T) = dim(V) implies T is bijective.
  • 2 Answer(s)
Answer Now
  • 0 Likes
  • 4 Comments
  • Shares
  • Shashi ranjan sinha thankyou
    no...... rank nullity theorem just gives the numerical relation between nullity,rank and dimension of domain if domain is finite dimensional....it also holds for linear transformat...
    Show more
    Likes(0) Reply(0)
  • Deepak singh thankyou
    no, this statement is not true.. rank nullity theorem does not implies bijective....
    Likes(1) Reply(0)
  • Sonika Jain
    mtlb acc to rank nulity theorm . its always true for any transformation that rank of t plus nullity of t is equal to dim of v . here when this condition is true implies transformat...
    Show more
    Likes(1) Reply(0)
  • Sonika Jain
    is this written always true
    Likes(1) Reply(0)