Math Is Fun Forum

virtualinsanity

Member

Registered: 2007-03-11

Posts: 38

Vector space problem (linear algebra)

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

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

Last edited by virtualinsanity (2007-04-17 05:16:19)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Vector space problem (linear algebra)

(a) False. The equation is only true for non-negative scalars a.

(b) False. This would imply that the real numbers were bounded below.

(c) True.