Let T be a nilpotent linear operator on the vector space \mathbb{ R}^5 (i.e., T^k=0 for some k). Let d_i denote the dimension of the kernel of T^i . Which of the following can possibly occur as a value of (d_1,d_2,d_3) ? 1. (1,2,3) 2. (2,3,5) , 3. (2,2,4) , 4. (2,4,5) For the excellent proof using Jordan Canonical form visit https://nbhmcsirgate.theindianmathematician.com/2020/04/nbhm-2020-part-c-question-26-solution.html#.XqCM3QR0R10.whatsapp Here we present a proof (incomplete in preciousness) on the fact "A linear transformation is completely determined by its behaviour on a basis."