Find a basis for the solution space of the given homogeneous system.

  1. 1. The problem statement, all variables and given/known data
    Find a basis for the solution space of the given homogeneous system.

    x1 x2 x3 x4
    1 2 -1 3 | 0
    2 2 -1 6 | 0
    1 0 0 3 | 0



    3. The attempt at a solution
    When I reduced to reduced row echelon form i get the following matrix:

    1 0 0 3 | 0
    0 1 0 0 | 0
    0 0 1 0 | 0

    Which I thought it meant that the basis for the solution space would be:

    1
    0
    0
    -3

    But apparently it isn't...what am I doing wrong?
     
  2. jcsd
  3. vela

    vela 12,444
    Staff Emeritus
    Science Advisor
    Homework Helper

    You didn't reduce the matrix correctly. Fix that first.
     
  4. I'm sorry I actually typed the matrix wrong when making this thread. The correct matrix is:

    1 2 -1 3 |0
    2 2 -1 6 |0
    1 0 3 3 |0
     
  5. Mark44

    Staff: Mentor

    Your reduced matrix says this:
    x1 = -3x4
    x2 = 0
    x3 = 0
    x4 = x4

    This means that any vector x in the solution space is a constant multiple of what vector?
     
  6. Ohh got it, seems pretty obvious now that i see it

    Thanks a lot btw
     
  7. Mark44

    Staff: Mentor

    You're welcome!
     
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