Question

S= (1,1), (1,2), (1,3), does it span R^2

Answer 1

Yes it spans it. Only two vectors would be required to span R^2 though.

Answer 2

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.

Answer 3

so does that mean any n number of vectors span in R^n, or are there situations where they don't span?

Answer 4

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)

Answer 5

They do not have to be orthogonal to each other though.

Answer 6

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.

Answer 7

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

Answer 8

thanks that make sense....