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

Solution space to homogenous equations.

  1. Dec 2, 2008 #1
    Ok so my question was:

    The directions state:

    Find the solution space of the following systems of linear homogeneous equations:


    Is the same as finding the solutions, because I did that and got (-z, -3z, 3z, z). So i said
    the solution space is actually the subspace you get. For instance, this problem yields a one dimensional subspace.
    And someone responded:

    I don't think that solution set is right.

    The vector -1,-3,3,1 does not give you 0 when used as weights in the original equation. It is a system of 4 unknowns in 3 rows there has to be a free variable somewhere. That means when you write your free variable in terms of the other variables, there should be a 0 in that solution set.

    The solution (-1,-3,3,1) does not satisfy ax=0.


    Am i right or am i wrong here?
  2. jcsd
  3. Dec 2, 2008 #2


    User Avatar
    Homework Helper

    I think you made an error somewhere. Substituting your answer into the first equation doesn't give 0. How did you get (-z, 3z, 3z, z) ?
  4. Dec 3, 2008 #3


    User Avatar
    Science Advisor

    I suggest you try that again. That is not at all what I get.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook