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Associated Homogeneous System definition

  1. Aug 19, 2010 #1
    Hi, thank you for viewing this thread. I have been googling for its definition for quite a while, but have not found any yet. Just wondering if there is a definition of it, in mathematical notations and in words?
  2. jcsd
  3. Aug 19, 2010 #2


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    Any system of linear equations can be written in the form
    [tex]a_{11}x_1+ a_{12}x_2+ \cdot\cdot\cdot+ a_{1n}x_n= b_1[/tex]
    [tex]a_{21}x_1+ a_{22}x_2+ \cdot\cdot\cdot+ a_{2n}x_n}= b_2[/tex]

    That is, the left side of each equation is a linear combination of the variables, and the right side is a number. The "associated homogenous system" is exactly the same with the numbers on the right side all set to 0.

    The "associated homogenous system" for the above system is:
    [tex]a_{11}x_1+ a_{12}x_2+ \cdot\cdot\cdot+ a_{1n}x_n= 0[/tex]
    [tex]a_{21}x_1+ a_{22}x_2+ \cdot\cdot\cdot+ a_{2n}x_n= 0[/tex]
    Last edited: Aug 19, 2010
  4. Aug 19, 2010 #3
    Alright, I got it. Thanks for your help!
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