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

Determine the number of solutions for a homogeneous system

  1. Dec 4, 2011 #1
    Hi all,

    I would like to know how to determine the number of solutions for a Homogeneous system.
    Ax = 0

    A is a m*n matrix and x is a n*1 vector.

    There are m equations and n unknowns. I'd like to know how to determine the number of solutions to this system.

    Thank you in advance.
     
  2. jcsd
  3. Dec 5, 2011 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    First, thinking of the m rows as vectors, determine how many of them are independent (the "rank" of A). Call that number m'. By the "rank-nullity" theorem, the nullity, the dimension of kernal(A), will be n- m'. The number of (independent) solutions will be 1 if [itex]n- m'\le 0[/itex], and n- m' if it is greater than 0.
     
  4. Dec 5, 2011 #3
    Thanks a lot for the answer...
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Determine the number of solutions for a homogeneous system
  1. Homogeneous system (Replies: 2)

Loading...