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Homework Help: Find a basis for a set S of R4

  1. Sep 26, 2012 #1


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    1. The problem statement, all variables and given/known data

    Find a basis for the subspace S of vectors (A+B, A-B+2C, B, C) in R4

    What is the dimension of S?

    3. The attempt at a solution

    Do I just plug in varying values for A B and C to create four vectors, and see if they are linearly independent? If they are then I've found a basis?
  2. jcsd
  3. Sep 26, 2012 #2
    Making any two of A, B & C zero results in a vector in S. How many such vectors are there?
  4. Sep 26, 2012 #3


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    Or, similar to voko's observation write it like this:$$
    A(1,1,0,0)+B(1,-1,1,0)+C(0,2,0,1)$$and see if that helps.
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