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How do i find the basis of subspace U

  1. Dec 6, 2008 #1
    1. The problem statement, all variables and given/known data
    In this case find the basis of subspace U
    1 2 3 4
    5 6 7 8
    -6 -8 -10 12

    2. Relevant equations
    elementary row operations

    3. The attempt at a solution
    alright, so i know i have to reduce the matrix and i have done so
    1 2 3 4
    0 1 2 3
    0 0 0 1
    now the answer i get is
    [1 5 -6]^T [2 6 -8]^T [4 8 12]^T
    but the answer in the back of my text book is
    [1 5 -6]^T [2 6 8]^T
    what have i done wrong, it seems they have one less column, is it my reduction of the matrix?
  2. jcsd
  3. Dec 6, 2008 #2
    You just had an error in reducing your matrix somewhere. Check over your work, because the matrix should have been
    1 0 -1 -2
    0 1 2 3
    0 0 0 0
    it was probably a simple algebra mistake.
  4. Dec 7, 2008 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    What "subspace U" are you talking about? You give an array of numbers which you refer to as a matrix. I can think of 4 different subspaces that might be meant here:

    The row space of the matrix.
    The column space of the matrix.
    The null space (kernel) of the matrix.
    The image of the matrix.

    Since you are row-reducing the matrix, you probably mean the column space but it would be a good idea to say so!
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