Can someone help me with these? Its for linear algebra, it is mostly quite intuitive

Recall, from the Week 4 Tutorial Activity: if U, W C V are subspaces such that every vector in v E U + W can be written uniquely v = u + w with u E U and w E W then we say that the sum U + W is direct and write U + W = UO W. Let T : V - V. Suppose we have an invariant subspace W, then we can restrict ourselves to simply looking at the subspace W and define the restriction operator Tw of T onto W. The restriction operator Tw : W - W is a linear transformation such that Tw (v) = T(v) for all v E W. Let T : V - V. Then T2 is defined as T2(v) = T(T(v)). Later we will prove that the composition linear transformations forms a linear transformation. Q1. Suppose that V is finite dimensional and let T : V - V be a linear map. In the previous assignment, we proved that the first three of these five statements are equivalent. Prove that all 5 statements are equivalent. (a) image(T2) = image(T) (b) ker(T) = ker (12 ). (c) image(T) n ker(T) = {0} (d) V = image(T) @ ker(T). (e) ker (Timage(T) ) = {0}. Q2. Suppose that Wi and W2 are subspaces of V with dim(W1) = n, dim(W2) = k, and n