3. Let L: V W be an isomorphism of vector spaces. Prove each of the following statements to show that L respects dimension, both of subspaces and of cosets, and the affine incidence structure in V and in W. This will verify that the model of affine geometry determined by an n-dimensional vector space V over F is isomorphic to the model of affine geometry deter- mined by FM (a) If U CV is a subspace with dim U = k, then L(U) CW is a subspace with dim L(U) = k. (b) If v +U is a k-dimensional coset in V, L(v +U) is a k-dimensional coset in W. (c) If A and B are objects in an affine space with ambient vector space V and AnB = C, then L(A) and L(B) are objects in an affine space with am nt vector space W and L(A) n L(B) = L(C). 3. Let L: V W be an isomorphism of vector spaces. Prove each of the following statements to show that L respects dimension, both of subspaces and of cosets, and the affine incidence structure in V and in W. This will verify that the model of affine geometry determined by an n-dimensional vector space V over F is isomorphic to the model of affine geometry deter- mined by FM (a) If U CV is a subspace with dim U = k, then L(U) CW is a subspace with dim L(U) = k. (b) If v +U is a k-dimensional coset in V, L(v +U) is a k-dimensional coset in W. (c) If A and B are objects in an affine space with ambient vector space V and AnB = C, then L(A) and L(B) are objects in an affine space with am nt vector space W and L(A) n L(B) = L(C)