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.
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  • 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...
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  • Deepak singh thankyou
    no, this statement is not true.. rank nullity theorem does not implies bijective....
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  • 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...
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  • Sonika Jain
    is this written always true
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