buckaroobill

04-17-2007, 02:02 PM

This problem was confusing me, so any help would be appreciated!

Here is a vector candidate. The set is R, and we define scalar multiplication by ax = a * x (usual scalar multiplication) and vector addition by x\oplusy = max(x, y).

For each of the following three vector space axioms, either verify the axiom or show that it does not hold.

a) a(x+y) = ax + ay

b) There exists an element 0 such that for any x in the proposed vector space, x + 0 = x.

c) x+y = y+x

Here is a vector candidate. The set is R, and we define scalar multiplication by ax = a * x (usual scalar multiplication) and vector addition by x\oplusy = max(x, y).

For each of the following three vector space axioms, either verify the axiom or show that it does not hold.

a) a(x+y) = ax + ay

b) There exists an element 0 such that for any x in the proposed vector space, x + 0 = x.

c) x+y = y+x