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September 23, 2020 7:24 pm 30 pts
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
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...
• Deepak singh
no, this statement is not true.. rank nullity theorem does not implies bijective....
• 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...