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)#
c#alpha# =(cx,cy,cz)
so c#alpha 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