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Homework Help: Basis physics homework

  1. Sep 13, 2005 #1
    let V = R^{4}. Consider the following subspaces:

    U = { (a,b,c,d) in R^{4} : a + 2b + 3c = 0, a + b + c + d = 0 }
    W = { (a,b,c,d) in R^{4} : a + d = 0, b + c = 0 }

    find a basis for U and a basis for W.

    i don't even know where to begin. Any help would be very much appreciated. Thanks.
  2. jcsd
  3. Sep 13, 2005 #2
    Look at the cooresponding matrix and reduce it to row-echelon form. The columns with pivots in them will be the same columns you use for your basis (remember, the same column... but from the ORIGINAL matrix).
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