Can some one help me with this (a clear proof with justifications if you dont mind so i can understand each step)

Assume that W is a subspace of a vector space V and that T: V->V is linear.
Suppose that V = R(T)+W ( V = the direct sum of R(T) and W) and W is T-invariant.
a) Prove that W is contained in N(T)
B) Show that if V is finite-dimensional, then W = N(T)
c) show by ex, that the concluson of b) is not necessarily true if V is not finite dimensional