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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


    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.
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