1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding a basis in ImT using Gaussian Elimination

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

    $$
    \begin{pmatrix}
    -1&3&0\\
    2&0&-1\\
    0&-6&1
    \end{pmatrix}
    $$

    Finding the ImT basis of this

    3. The attempt at a solution

    I got it down to

    $$
    \begin{pmatrix}
    1&0&-1/2\\
    0&1&1/6\\
    0&0&1
    \end{pmatrix}
    $$

    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.

    Josh
     
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding a basis in ImT using Gaussian Elimination
  1. Gaussian elimination (Replies: 2)

  2. Gaussian Elimination (Replies: 11)

  3. Gaussian elimination (Replies: 2)

  4. Gaussian elimination (Replies: 3)

Loading...