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."