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Homework Help: Dimension of a subspace question

  1. Apr 16, 2012 #1
    I'm a little confused about some of the matrix terminology.
    I have the following subspace:

    span{v1, v2, v3} where v1, v2, v3 are column vectors defined as:

    v1 = [1 2 3]
    v2 = [4 5 6]
    v3 = [5 7 9]
    (pretend they are column vectors)

    How am I supposed to find the dimension of the span?

    My Work:

    I created a 3x3 matrix using the column vectors, then I performed row operations to get it into upper triangular form. After performing these row operations, I ended up with the resulting matrix:
    [1 4 5
    0 -3 -3
    0 0 0 ]

    So because the rank(A) = 2, the dimension is 2. Am I right?
    Also, how would I go about finding the basis vectors. Thank you.
  2. jcsd
  3. Apr 16, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper

    If you are going to do row reduction put your vectors into the matrix as rows. So yes, you'll get dimension 2. The two nonzero rows will be basis vectors.
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