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Homework Help: Find the basis for the row space

  1. Jul 9, 2011 #1
    1. The problem statement, all variables and given/known data

    Find the basis for the row space

    3. The attempt at a solution

    the given matrix is

    0 1 2 1
    2 1 0 2
    0 2 1 1

    So i reduced to row-echeleon form

    2 1 0 2
    0 1 2 1
    0 0 3 1

    so then rank = 3. My textbook states that the basis of the row space are the row vectors of leading ones, hence the basis for row space is
    { [2,1,0,2], [0,1,2,1], [0,0,3,1] }

    however my textbook has this answer
    { [6,0,0,5], [0,3,0,1]. [0,0,3,1] }

    HOW?!!?!?!!?!?! :-(

    edit: NVM figured it out. Didnt realize the textbook reduced the matrix to reduced row form.
     
    Last edited: Jul 9, 2011
  2. jcsd
  3. Jul 10, 2011 #2

    lanedance

    User Avatar
    Homework Helper

    also worth noting any linearly independent set of vectors that spans the space is a basis. In general there is no unique basis
     
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