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Proof on homogeneous equations

  1. Dec 4, 2007 #1
    I need some help here... I've got the following assignment to do

    Prove that if M>N then any system of N homogeneous equations in M unknowns has many solutions.

    I am a bit stuck with this one. I thought about creating a MxN Matrix and to display the determinant with 1's.

    and then say about the remaining colums after the rows with leading 1's stop (r = M-N), that they can represented by any value so there are many solutions
    is that correct?
  2. jcsd
  3. Dec 4, 2007 #2
    i don't know what you're saying but yes if you write down a matrix with M columns and N rows you'll see that you have a linearly dependent set of vector spanning the column space hence many solutions.
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