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Null(A) and cartesian form.

  1. Mar 22, 2010 #1
    Hi there,

    just a pretty straight forward query I need cleared up.....

    If a question asks for the null space of A in cartesian form how do I set it out?

    This is what I've got:

    X = ( -2; 1; 1)*x3 for all values of x3

    Therefore, Null(A) corresponds geometrically to the line through the origin and (-2, 1, 1).

    Now do I need to say that this is equivelant to -x = 2y = 2z for it to be in cartesian form or will the above suffice?

    thanks for the help
  2. jcsd
  3. Mar 22, 2010 #2


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    I'm a bit confused. What is A, and how does that compare to X? Is X supposed to be the one dimensional vector space through the vector (-2,1,1)?
  4. Mar 22, 2010 #3
    Yes, so AX = 0

    where X = ( x1; x2; x3) and A = (1 0 2; 0 3 -3; 4 2 6)

    which can be expressed as ( -2; 1; 1)*x3 after row reduction and back substitution.

    I need to know whether I can leave it at that, or express it as the line: -x = 2y = 2z
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