Question 6. Let V be a nite dimensional vector space and T, U : V > V be non-zero linear maps that satisfy R(T) R(U) = {0}. Prove that T and U are linearly independent in (V), the space of linear maps from V to V. [Hint: when are two vectors u, v linearly dependent? Apply the conclusion to T, U E (V). Make explicit use of the fact that the maps are nonzero]