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Comfusing me

  1. Dec 3, 2007 #1
    have a matrix:

    X1+X2+X3+X4 = 0
    X1+X2-X3-X4 = 0
    X1-X2+X3-X4 = 0

    the solutions that are formed are:

    Now i understand that they just used t to label the free variables.. but Iam not sure how they were able to tell which were negative and positive.. I tried to do it out, but just confused myself more.. Help anyone?
  2. jcsd
  3. Dec 4, 2007 #2
    The answer means:
    X1 = t
    X2 = -t
    X3 = -t
    X4 = t

    The reason for the signs is they have to add to zero in all three cases.

    For instance:
    Take X1+X2+X3+X4

    If you substitute the answer in you get:

    t+ (-t) + (-t)+t

    t+(-t) is zero and (-t)+t is zero so they add to zero.

    In the second case:


    In this case substituting in the answer:

    t + (-t) - (-t) - t

    t + (-t) is zero and -(-t)-t is zero

    The third case is left as an exercise for the student.
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