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Homework Help: Finding a basis in ImT using Gaussian Elimination

  1. May 19, 2012 #1
    1. The problem statement, all variables and given/known data


    Finding the ImT basis of this

    3. The attempt at a solution

    I got it down to


    I know that by the principle of having pivots as the only non-zero entities in their respective columns this makes that column one of the basis vectors. So answer is

    [-1,2,0] [3,0,-6]

    What i don't understand is why (In the r-echelon form) i cannot subtract -1/2(Row 3) from Row 1 and Subtract 1/6(Row 3) from Row 2 to give the Guass-Jordan form or Identity form which would imply that the entire first matrix was a basis for itself right? Meaning the basis contains three vectors instead of the actual two is contains in the correct answer.

    Thanks, and i hope the question has come out clearly, just say if clarification is needed.

    Last edited: May 19, 2012
  2. jcsd
  3. May 19, 2012 #2
    What is 'ImT basis'?
    The image of some basis under T?
  4. May 19, 2012 #3
    No it's just the basis over T i guess. The generic basis that spans T(v) where v is an arbitrary vector and the matrix for T is the above.
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