4. Recall the weird vector space given in Question 1 of Assignment 2: V = R with operations defined by (u, U2)+(V1, V2) = (u +v+1, 2+2 -1) k(u, u) = (ku+k-1, kuz-k+1) Let u (1,0), = (-1,0). = (a) Show that (u, v) form a basis in V (you must use these weird operations.) (b) Find the coordinate vectors of (2,0) and (0,0) and (-1, 1) relative to this basis (again, you must use these weird operations.)