Suppose V is a vector space and T:VarrowV is a linear transformation. It is also known that dim(V)=n. Let v be a vector in V such that T^k(v) does not equal zero vector, k=1,2,.....,n-1, however, T^n(v) equals aero vector. Prove that {v, Tv, T^2V,...,T^n-1v} is a basis of V. It is understood that T^k equals the composition of itself k times.