1. Limited time only! Sign up for a free 30min personal 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 system

  1. Apr 15, 2013 #1
    Hi,
    I'm solving out a homogeneous 3 equations and 4 variables system so I considered one variable as known term but the determinant of the matrix is 0, how do I use Cramer in this case ?
    these are the 3 equations

    2x + 3y - z - 2v = 0
    4x - 3y - 5z + 5v = 0
    8x + 3y - 7z + v = 0

    determinant of {{2,3,-1},{4,-3,-5},{8,3,-7}} is 0

    thanks
     
  2. jcsd
  3. Apr 15, 2013 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The normal way to solve a system like this would be to use row reduction.
     
  4. Apr 15, 2013 #3
    but how can I solve it with Cramer ?
     
  5. Apr 15, 2013 #4

    Mark44

    Staff: Mentor

    I don't think there is any reason that you should assume that one variable is known. This is apparently a system of three equations in four unknowns. The matrix of coefficients isn't square, so the concept of the determinant doesn't apply, and you can't use Cramer's Rule.
     
  6. Apr 15, 2013 #5

    Mark44

    Staff: Mentor

    As already noted, Cramer's Rule doesn't apply here. Follow the advice that LCKurtz gave.
     
  7. Apr 15, 2013 #6

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Also note that it isn't obvious just looking at the system whether there might be 1 or more free variables. You really need row reduction to answer that.
     
  8. Apr 16, 2013 #7

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Cramer's rule only applies when the determinant of coefficients is nonzero. No matter which column you omit, the resulting 3x3 matrix has zero determinant, so in this question Cramer's Rule fails in every single case you try.

    As others have suggested, just use row reduction; but an equivalent description would be: just use the variable-elimination method as taught in high school.
     
    Last edited: Apr 16, 2013
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Homogeneous system
  1. Homogeneous system (Replies: 6)

  2. Homogenous system (Replies: 7)

  3. Homogenous linear system (Replies: 12)

Loading...