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

Mathematics
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they said I have to satisfy two conditions but Idk how to apply it
how do you define 'subspace'. what properties do we look for?
like for example I have this question in a book that says it is not a subspace. |dw:1443912367126:dw|

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subspace of R^2 for that problem^
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
So basically what factors define an area of R\(^2\) ?
so closed under addition and scalar multiplication
I guess so..?
is -(x1,x2) in the vector space?
I'm guessing no? because x1 and x2 should be greater than 0?
thats what im thinking to and there is no restriction in the value of our scalar is there?
(-x1, -x2) is not in the defined set
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?
correct, if the properties are not satisfied in order to be defined as something, then we cannot claim that it exists as that thing.
calling a cat a tree, is not valid logic is it :)
lol okay, I think I get it now, thank you! :D
good luck

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