buckaroobill
New member
- Joined
- Dec 16, 2006
- Messages
- 40
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\(\displaystyle \oplus\)y = 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\(\displaystyle \oplus\)y = 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