Complete the proof to the right that the zero vector is unique axioms in the following axioms, u, v, and w are in vector space v and c and d are scalars. suppose that w in v has the property that u +w-w 0+w w+0by axiom 1, and w + 0-wby axiom type whole numbers.) ll u in v. in particular, 0+ w o. but . hence, w-w+0-o-w-o 1. the sum uv is in v 3. (u+v)+w ut(v+ w) 4. vhas a vector 0 such that u + 0 = u 5. for each u in v, there is a vector -u in v such that u-u)-0. 6. the scalar multiple cu is in v. 8. (c+d)u cu+ du 9, c(du) = (cd)u 0 u-u