# Thread: Proving that a subset of R^3 is a subspace (or not), and proof critique.

1. ## Proving that a subset of R^3 is a subspace (or not), and proof critique.

(1) For each of the following subsets of R^3, prove that it is a subspace or prove that it is not a subspace.

https://imgur.com/a/WIfqmDj

Did I get it right?

I'm especially concerned with the first part, I don't think I did that right..

2. ## Re: Proving that a subset of R^3 is a subspace (or not), and proof critique.

You are making the first part too hard. The zero vector [0,0,0] is trivially of the form [0,x,y]. It has nothing to do with A. The rest looks OK.

3. ## Re: Proving that a subset of R^3 is a subspace (or not), and proof critique.

So, though unnecessary, is that the first part correct?

4. ## Re: Proving that a subset of R^3 is a subspace (or not), and proof critique.

Originally Posted by MrJank
So, though unnecessary, is that the first part correct?
No. I would not give credit for that argument because it misses the point.

5. ## Re: Proving that a subset of R^3 is a subspace (or not), and proof critique.

Originally Posted by Walagaster
No. I would not give credit for that argument because it misses the point.
Ok, I'm confused how to write it then. Would I just take a vector x from the subset and make its elements = to zero?

6. ## Re: Proving that a subset of R^3 is a subspace (or not), and proof critique.

Yes. I would phrase it something like this: $L = \{[a,b,c]|a=0\}$ To see that $[a,b,c]=[0,0,0]\in L$ just note that $a=0$.
(I have used rows instead of columns to save typing. The idea is the same.)

7. ## Re: Proving that a subset of R^3 is a subspace (or not), and proof critique.

The set of vectors, [a, b, c] with the condition that a= 0 is just the set of all [0, b, c] where b and c can be any numbers. In particular, b and c can be 0 which gives the zero vector, [0, 0, 0].