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Homework Help: Basis R 2

  1. Feb 27, 2010 #1
    Find the basis of the vector space (1,2)^T; (-1,1)^T

    When I solve the matrix, I obtain x1=0 and x2=0


    Can a basis be two 0 column vectors? Thanks for the help.
  2. jcsd
  3. Feb 27, 2010 #2
    No, a basis cannot be two 0 column vectors.
    What matrix are you talking about? Are you trying to solve (1,2)x1 + (-1,1)x2 = 0? If so, what does this tell you?
    And what does the vector space look like? Is it the span of those two vectors? Is this span minimal?
  4. Feb 27, 2010 #3
    All the question says is to determine the basis. I am then given two column vectors (1,2) and (-1,1).

    I solved the augmented matrix and obtained that both x1=0 and x2=0.
  5. Feb 27, 2010 #4
    And what does x1 = 0 = x2 tell you? You are trying to determine if the two vectors are linearly independent, so you are solving the system (1,2)x2 + (-1,1)x2 = 0. Thus, a solution of (x1, x2) = (0, 0) tells you something about the vectors (1,2) and (-1,1).
  6. Feb 27, 2010 #5
    I know they are independent from the det not equaling 0. I am trying to find the basis of the vector space.
  7. Feb 27, 2010 #6
    What does the vector space look like? You have only identified two vectors. Is it the set of linear combinations of these two vectors?
  8. Feb 27, 2010 #7
    I have giving you all the information. What are you asking for? It is in R^2 but that is also mentioned in the title.
  9. Feb 27, 2010 #8


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    The phrase "the basis of the vector space (1,2)^T; (-1,1)^T" doesn't make sense. R2 is the vector space; (1,2)^T; (-1,1)^T are two vectors, not a vector space. It's not really clear what you're trying to do.
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