Question

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

Answer 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