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

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