1. The problem statement, all variables and given/known data If we define V as the set of vectors in R^2 with vector addition defined as it normally is, but scalar multiplication defined to be k(a,b)=(k2a,k2b), then V is not a vector space. Find all axioms that fail (and explain why they fail). 2. Relevant equations Axioms: 1. If u and v are objects in V, then u+v is in V. 2. u+v = v+u 3. u+(v+w)=(u+v)+w 4. There is an object 0 in V, called a zero vector for V, such that 0+u=u+0=u for all u in V. 5. For each u in V, there is an object -u in V, called a negative of u, such that u+(-u)=(-u)+u=0. 6. If k is any scalar and u is any object in V, then ku is in V. 7. k(u+v)=ku+kv 8. (k+l)u=ku+lu 9. k(lu)=(kl)u 10. 1u=u 3. The attempt at a solution I couldn't figure out how to start.