Let p be an odd prime (i.e., any prime other than 2). Form twovector spaces V1, V2 over Fp(prime field of order p) with bases corresponding to the edges andfaces of an icosahedron (so that V1 has dimension 30 andV2 has dimension 20). LetT : V1 ? V2 be the linear transformationdefined as follows: given a vector v ? V1, T(v) is thevector in V2 whose component corresponding to a givenface is the sum of the components of v corresponding to the edgesaround that face. Prove that T is surjective. (Hint: one option isto look closely at the five edges emanating from a singlevertex.)
