anonymous
  • anonymous
S= (1,1), (1,2), (1,3), does it span R^2
Mathematics
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Yes it spans it. Only two vectors would be required to span R^2 though.
anonymous
  • anonymous
If you could pick any point in R^2 and write it as a combination of these vectors, then it spans R^2. If you couldn't, then it doesn't.
anonymous
  • anonymous
so does that mean any n number of vectors span in R^n, or are there situations where they don't span?

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anonymous
  • anonymous
There are situations where they wouldn't. R^3 would be spanned conventionally by [1 0 0], [0 1 0], [0 0 1]. There must be a vector to define every possible point in the span, so [2 0 1] [0 0 1] [1 0 1] would not span R^3 because it could not define any point of the form (0 x 0)
anonymous
  • anonymous
They do not have to be orthogonal to each other though.
anonymous
  • anonymous
what do you mean (0x0), 0x(2 0 1) + 0x(0 0 1) + 0x(1 0 1) isn't that a possibility? I am sorry I am so confused.
anonymous
  • anonymous
I meant any point of the form (0 n 0) where n is any number would not be definable in the the second set of vectors. I used x before. I am sorry it was confusing. Look at http://tutorial.math.lamar.edu/Classes/LinAlg/Span.aspx maybe it will help
anonymous
  • anonymous
thanks that make sense....

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