Please refer to the question below. Note: This is all that the question comes with!

Question 1. a, lpt) Let V, W be vector spaces and T,S : V > W be linear transformations. Let 1:1, .. Hum E V. Prove that if TIME) = Sims) for each i = 1, . .. ,m, then T(1r}= 3(1)} for all I: E spanm. . . ,vm). bI lpt) Let U be a vector space and u, tnw be three linearly independent vectors in U. Is there a linear operator R : U r U such that 3(a) = w, 3(a) = u, and R(2u 30) = ta? Explain your reasoning