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!

Linear Algebra solution to a system of equations

  1. Oct 15, 2013 #1
    1. The problem statement, all variables and given/known data

    x + y+ z = 0
    3x + 2y -2z = 0
    4x + 3y -z = 0
    6x + 5y + z = 0

    2. Relevant equations



    3. The attempt at a solution

    I put the equations into a matrix and reduced to RREF. This is what I end up with:

    x - 4z = 0
    y + 5z = 0

    The other two rows in the matrix are all zeroes.

    I've never solved a system that had more equations than unknowns, so I'm confused on how many free variables I will need. Right now I have this as my solution:

    x = 4t
    y = -5t
    z = t
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 15, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    And that is just fine as a solution. There are really only two independent equations in there. The third one is the sum of the first two equations. The fourth is three times the first equation added to the second. They are redundant, as your RREF showed you.
     
    Last edited: Oct 15, 2013
  4. Oct 17, 2013 #3
    If you write the system of the equations in matrix form and you perform elementary row operations and put the matrix into row reduced echelon form then what is the rank of the matrix ? (Hint...which columns are independent and which are dependent ?) If the rank is r and the number of columns is n then n-r = the dimension of the nullspace for the coeficient matrix = the number of free variables. In this case the dimension for the nullspace is 1 since n - r = 3 - 2 = 1 and a basis for the nullspace is the vector c(4, -5, 1). So if c = 1 then x = 4, y = -5, z=1 is a solution. In other words you are correct.
     
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: Linear Algebra solution to a system of equations
Loading...