owlet
  • owlet
How to determine whether a set of vectors is subspace of R^n or not? I'm confused about this topic.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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owlet
  • owlet
they said I have to satisfy two conditions but Idk how to apply it
amistre64
  • amistre64
how do you define 'subspace'. what properties do we look for?
owlet
  • owlet
like for example I have this question in a book that says it is not a subspace. |dw:1443912367126:dw|

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owlet
  • owlet
subspace of R^2 for that problem^
owlet
  • 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
Jhannybean
  • Jhannybean
So basically what factors define an area of R\(^2\) ?
amistre64
  • amistre64
so closed under addition and scalar multiplication
owlet
  • owlet
I guess so..?
amistre64
  • amistre64
is -(x1,x2) in the vector space?
owlet
  • owlet
I'm guessing no? because x1 and x2 should be greater than 0?
amistre64
  • amistre64
thats what im thinking to and there is no restriction in the value of our scalar is there?
amistre64
  • amistre64
(-x1, -x2) is not in the defined set
owlet
  • 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?
amistre64
  • 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.
amistre64
  • amistre64
calling a cat a tree, is not valid logic is it :)
owlet
  • owlet
lol okay, I think I get it now, thank you! :D
amistre64
  • amistre64
good luck

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