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Homework Help: Uniqueness of a vector

  1. Mar 5, 2008 #1
    1. The problem statement, all variables and given/known data
    Determine if the vector x is unique.

    x = (-15, -3, 0) + x_3 (10, 0, 1)

    Note: The scalars should be vertically placed instead of horizontal.

    3. The attempt at a solution

    Seeing that there is a free variable, I said that x is not unique, but my teacher marked it wrong. Why is it unique, and in what case would it not be unique?
     
    Last edited: Mar 5, 2008
  2. jcsd
  3. Mar 5, 2008 #2
    So, x_3 is the 3rd component of x correct? If that's the case (I don't see what else it could be) then I agree that it doesn't seem to be unique as we have

    (1) x_1 = -15 + 10t
    (2) x_2 = -3
    (3) x_3 = t

    Now t can be chosen to be any real number. Are you sure that you copied them correctly?
     
    Last edited: Mar 5, 2008
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