Determine if subset is subspace of R3. Need Help.

[digitol87]

1. {[x,y,z] | x,y,z in R, z = 3x+2}.
How do I determine if this subset is a subspace of R3? Am I wrong when I say this set contains the zero vector? If this is the case, then I have to use the addition and multiplication closure methods, right?

Thanks

 

[Mark44]

{[x,y,z] | x,y,z in R, z = 3x+2}.
How do I determine if this subset is a subspace of R3? Am I wrong when I say this set contains the zero vector?

Yes, wrong. (0, 0, 0) does not satisfy z = 3x + 2.

If this is the case, then I have to use the addition and multiplication closure methods, right?

Thanks

 

[digitol87]

Yes, wrong. (0, 0, 0) does not satisfy z = 3x + 2.

OK, That's a good first step. I'm still a little confused as to how to apply the addition method.
can I add [x,y,z] + [a,b,c] then get [x+a, y+b, z+c] ? Then what?

Thanks.

 

[Mark44]

No, you have to take two elements in the set, and show that their sum is in the set. You can't take any old arbitrary vector in R³. Also, it must be true that if v is an element in the set, then kv is also in the set.

What must be true for any element in your set? I.e., how do you distinguish between vectors in your set and plain old vectors in R³?