# Let V=#RR^3# and W={(x,y,z)|x,y,z #in# #QQ#}. Is W#<=#V? Justify your answer.

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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