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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
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- 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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Deepak singh 1
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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 transformation to be bijective that means every transformation is always bijective ???
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Sonika Jain
is this written always true
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Shashi ranjan sinha![best-answer]()
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 transformations which are not bijective.... You can easily construct easy non bijective linear transformations satisfying rank nullity theorem