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!

Homework Help: Simple question regarding general solutions

  1. Feb 11, 2013 #1
    1. The problem statement, all variables and given/known data
    Solve the homogeneous system of equations.


    2. Relevant equations
    The relevant matrix is like so:
    1 0 0
    -1 0 0
    3-5 0


    3. The attempt at a solution
    Add R1 to R2, then add -3R1 to R3.

    1 0 0
    0 0 0
    0-5 0

    Interchange R2 and R3, then divide the new R2 by -1/5

    1 0 0
    0 1 0
    0 0 0

    Under other circumstances where there's a general solution to such a matrix, with a row of zeroes on the bottom, but not an empty column for x3, you would write x3=r or what have you and then include r when solving for x1 and x2. In this case, where x1 and x2 simply equal zero, what would one write about x3?
     
    Last edited: Feb 11, 2013
  2. jcsd
  3. Feb 11, 2013 #2

    Mark44

    Staff: Mentor

    x3 is arbitrary, meaning it can have any value.
     
  4. Feb 11, 2013 #3
    In this case, you still have to set ##x_3 = r## for some ##r \in \mathbb{R}##.
     
  5. Feb 11, 2013 #4
    Thank you both.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...