Zero element/unit element

1. Sep 12, 2006

indigojoker

Let R^2 be a set containing all possible rows: (a b)

when using the 8 axioms to prove whether (a,b) is indeed a vector space, i have to show that there is a zero element and a unit element.

Is the zero element 0? or is it in matrix form such that W = (0 0) and W is contained in R^2?

Is the unit element 1? or is it in matrix form such that F=(1 1) and F is contained in R^2?

If I showed the 8 axioms are true, then does that show that R^2 is indeed a vector space?

2. Sep 12, 2006

ircdan

And yes just show the 8 axioms hold.

Last edited: Sep 12, 2006
3. Sep 13, 2006

HallsofIvy

Staff Emeritus
No, he's not right about (1, 1).

indigojoker, you shouldn't even have to think about that. The "zero element" acts like 0: x+ 0= 0 in the VECTOR addition. If you are adding vectors the 0 has to be a vector: (0, 0). On the other hand, scalar multiplication involves multiplying a scalar by a vector: in "1v= v", the "1" is a number, not a vector.