$ 1) T is a linear transformation in $ L(U,V) $ and $ u_1, u_2,..u_n \in U. $ Given that $ T(u_1), T(u_2)...T(u_n) $ are linear independent elements of V, prove that $u_1,u_2...u_n $ are also linear independent. Also prove the converse is false. $
$ 2) Prove that the Eigenvalues of an n x n...