I am stuck on this problem. How can I resolve this?

Results for this submission Entered Answer Preview Result Let u, v, and w be arbitrary vectors in V. 2 Assume u + w = v + w. Adding -w to both sides of the equation, we have (see preview) (u + w) + (-w) =(v+ w)+(-w). Applying axiom (A2) (the associative law) to both sides of the equation, we have incorrect u+(w+(-w))=v+(w+(-w)). Applying axiom (A4) (the law of additive inverses) to both sides of the equation, we have U = V. The answer above is NOT correct.(1 point) In this problem, you will prove the cancellation law of Proposition 9.9: Theorem. Let / be a vector space over some field K . For vectors u, v, w: if u + w = v + w, then u = v. Put 10 of the following sentence fragments in order to form a logically correct proof of the theorem. There is only one correct answer, so be sure not to skip any steps. Choose from these: Proof of the theorem: u+0=v+0. Let u, v, and w be arbitrary vectors in V. Homework 2 utw=v+w. Assume u + w = v + w. (-1 )(u + w) = (-1)(v + w). Adding -w to both sides of the equation, we have Multiplying both sides of the equation by -1, we (ut w) + (-w) =(v+w)+(-w). have Applying axiom (A2) (the associative law) to both Adding w to both sides of the equation, we have sides of the equation, we have Assume u = V. u+(w+(-w))=v+(w+(-w)). Applying axiom (A1) (the commutative law) to both Applying axiom (A4) (the law of additive inverses) sides of the equation, we have to both sides of the equation, we have0tu=0+v. u = V. Applying axiom (A3) (the additive unit law) to both sides of the equation, we have w+u=w+v. Homework 2 n+w/v+w