Let V=RR^3 and W={(x,y,z)|x,y,z in QQ}. Is W<=V? Justify your answer.
So far, I wrote:
1. (0,0,0)in W
2.alpha ,beta in W
alpha =(x,y,z) beta =(x',y'z')
alpha,beta =(x+x',y+y',z+z')
so alpha + beta in W
3. c in RR , alpha in W
alpha=(x,y,z)
calpha =(cx,cy,cz)
so calpha in W
Hence, W <= V
So far, I wrote:
1. (0,0,0)
2.
so
3. c
c
so c
Hence, W
1 Answer
It looks like you are trying to show that
Explanation:
If you restricted yourself to showing that
For vector (linear) spaces, the problem is with the scalar multiplication. Since
On the other hand, if your field of scalars was