Hello,

I am stuck with this problem.

prove that the union of two subspaces of the vector space is a subspace ofif and only ifone of the subspaces is contained in the other.

Thanks in advance for your help.

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- Aug 4th 2010, 02:01 PMakolmanVector Subspaces Union problem
Hello,

I am stuck with this problem.

prove that the union of two subspaces of the vector space is a subspace of**if and only if**one of the subspaces is contained in the other.

Thanks in advance for your help. - Aug 4th 2010, 02:07 PMAckbeet
Can you prove that if one subspace is contained in the other, the union is a subspace? That should be relatively straight-forward.

- Aug 4th 2010, 02:16 PMakolman
Yes, I think I get that part. Is it right like this?

If and are subspaces of and .

Then .

So is a subspace of

But how would you the other way. Assuming first that the union of two subspaces, say and , of the vector space . Then how do you prove that one of them is contained in the other? - Aug 4th 2010, 02:23 PMPlato
Suppose that is a subspace and .

We know that .

What is wrong with that? - Aug 4th 2010, 02:39 PMakolman
If and , then and . That would be assuming that the subspaces are not contained.... but I am still lost on how to continue.

- Aug 4th 2010, 02:59 PMPlato
Is it true that

Is it true that

There is a contradiction there. What is it?