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New to Linear Algebra

  1. Aug 23, 2009 #1
    1. The problem statement, all variables and given/known data

    suppose x=x0+tv and y=y0+sw are two parametric representations of the same line l in r^n
    a. show that there are scalars t0 and s0 such that y0=x0+t0v and x0=y0+s0w
    b. show that v and w are parallel


    3. The attempt at a solution

    a. same line thus
    y0+sw=x0+tv
    when s0w=t0w then y0=x0 (essentially the solution...I think)

    b. not sure at all
    I don't like saying because the problem states: parametric rep of same line then must be parallel, but this is the most obvious statement to me
     
  2. jcsd
  3. Aug 23, 2009 #2

    Tom Mattson

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    For part b pick any two points on the line [itex]x_1[/itex] and [itex]x_2[/itex] corresponding to [itex]t_1[/itex] and [itex]t_2[/itex], respectively. Since the second parameterization is of the same line then there must exist [itex]s_1[/itex] and [itex]s_2[/itex] such that [itex]y_1=x_1[/itex] and [itex]y_2=x_2[/itex], respectively. Can you take it from there?
     
  4. Aug 23, 2009 #3
    leading us to the idea that y1-x1=y2-x2 meaning 0=0, thus parallel
     
  5. Aug 23, 2009 #4

    Tom Mattson

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    No, you need to slow down and be more careful. You're trying to show that w is parallel to v, which means that w is a nonzero scalar multiple of v.
     
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