# Vector space

1. Oct 8, 2007

### skydiver_spike

rather than use the standard definitons of addition and scalar multiplication in R^2, suppose these two operations are defined as follows.
(x1,y1)+(x2,y2)=(x1,0)
c(x,y)=(cx,y)

what would the zero vector be? can it be (0,-y1)? why or why not? I think it should fail this axiom u+0=u.

2. Oct 8, 2007

First of all, your addition, as defined, is not commutative, i.e. (x1, y1) + (x2, y2) = (x1, 0) $\neq$ (x2, y2) + (x1, y1) = (x2, 0).