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## owlet one year ago How to determine whether a set of vectors is subspace of R^n or not? I'm confused about this topic.

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1. owlet

they said I have to satisfy two conditions but Idk how to apply it

2. amistre64

how do you define 'subspace'. what properties do we look for?

3. owlet

like for example I have this question in a book that says it is not a subspace. |dw:1443912367126:dw|

4. owlet

subspace of R^2 for that problem^

5. owlet

It says here... there are rules that must be satisfied to know if something is a subspace of R^2: $x + y \in S\\ tx \in S$ x and y are vectors

6. anonymous

So basically what factors define an area of R$$^2$$ ?

7. amistre64

so closed under addition and scalar multiplication

8. owlet

I guess so..?

9. amistre64

is -(x1,x2) in the vector space?

10. owlet

I'm guessing no? because x1 and x2 should be greater than 0?

11. amistre64

thats what im thinking to and there is no restriction in the value of our scalar is there?

12. amistre64

(-x1, -x2) is not in the defined set

13. owlet

So it means, I just have to check the conditions in the given set if they follow those two rules? If they don't follow it, then it is not a subspace? am i understanding it right?

14. amistre64

correct, if the properties are not satisfied in order to be defined as something, then we cannot claim that it exists as that thing.

15. amistre64

calling a cat a tree, is not valid logic is it :)

16. owlet

lol okay, I think I get it now, thank you! :D

17. amistre64

good luck

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