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Problem in setting homogenous parameters

  1. Nov 13, 2009 #1
    1. The problem statement, all variables and given/known data

    how to put x+z=0, and y-z+2w=0 into matrices in terms of two parameters?


    2. Relevant equations
    AX=0, looking for x


    3. The attempt at a solution

    x=-z
    y=z-2w

    (-1, 1, 1, 0)z, no idea what the other matrix is :S

    thanks advance guys!
     
  2. jcsd
  3. Nov 13, 2009 #2

    Mark44

    Staff: Mentor

    Your question is somewhat misleading. I don't think you want to put the equations into matrices, but rather find two vectors that are a basis for the nullspace (or kernel) of your matrix A.

    You can write z and w in terms of x and y, like so:
    z = -x
    w= -.5x -.5y
    In the latter equation, I substituted -x for z in the equation y -z + 2w=0.


    x=1x+0y
    y=0x+1y
    z=-1x+0y
    w=-.5x-.5y

    So in the equations above, a vector x = (x, y, z, w) can be written as a linear combination of two other vectors.
     
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