give an example of two distinct linear operator on the same vector space which have same kernel and image​

1 thought on “give an example of two distinct linear operator on the same vector space which have same kernel and image​”

1. Answer:

   Let T and L linear operators with vector space V such that Im(T)=Im(L) and Ker(T)=Ker(L) show that L=T

   Since they are linear operators

   T:V→V and L:V→V

   Base is {α1,⋯,αr} of Ker(T) base completed of V wiht {αr+1,⋯,αn} and {Tαr+1,⋯,Tαn} is base of Im(T) but I can not think like finding equality

   this the process plz solved it

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