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# Subspaces of R^n watch

1. I'm kinda stuck on this question:

Let be subspaces of and let

(i) Is a subspace?

(ii) Prove that is a subspace if, and only if or

I've managed to do part (i), and prove the "only if" part of (ii), although I'm struggling on the "if" part of part (ii). I'm given the hint:

if consider any vectors , and prove that , hence .

My problem is proving that the sum doesn't lie in or . Could anyone point me in the right direction?
2. If then since we must have (as it's a subspace), and then... [do the same with and derive a contradiction from here].
3. cheers ...i had a feeling thered be some sort of contradiction, just didn't know how to go about it.

Out of curiosity, why does this require ?

If one of them was ={0}, wouldn't that just imply that which is a subspace, and = whichever one isn't equal to 0 (or 0 if they're both 0) and thus also a subspace?

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Updated: April 4, 2011
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