Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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]
    etc.

    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]
    etc.
     
    Last edited: Aug 19, 2010
  4. Aug 19, 2010 #3
    Alright, I got it. Thanks for your help!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Associated Homogeneous System definition
  1. Homogeneous system (Replies: 2)

Loading...