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!

Homogeneous linear system

  1. Aug 2, 2008 #1
    I have a question:
    If the vectors of v & u are solutions of the nonhomogeneous linear system Ax=b, then ru+sv is a solution of the nonhomogeneous system for any real values of r and s.
    is this statement true?
    is this statement true for homogeneous systems too?
     
  2. jcsd
  3. Aug 2, 2008 #2
    Hint: When a nonhomogeneous linear system has infinite solutions, then the general solutions can be written in parametric vector form.

    This can be used to answer both questions.
     
  4. Aug 2, 2008 #3

    Defennder

    User Avatar
    Homework Helper

    You should be able to find a counterexample easily for the first question. For the second, try writing the matrix equation for Ax=b using ru+sv.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Homogeneous linear system
Loading...