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Does a set of vectors span Rn

  1. Oct 11, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine if the following sets of vectors span the indicated space

    a) {[0 -6 -6], [8 -3 5], [-9 7 -2]}, ℝ3.
    b) {[2 1 7 -2], [3 5 4 5], [4 -4 -3 -3], [-5 0 6 -4]}, ℝ4.

    2. Relevant equations



    3. The attempt at a solution
    a) a[0 -6 -6] + b[8 -3 5] + c[-9 7 -2] = [x y z]
    x = 8b - 9c
    y = -6a -3b + 7c
    z = -6a + 5b - 2c

    I don't know where to go from here - I'm sure if I can figure that out I'll be able to do b as well.
     
  2. jcsd
  3. Oct 11, 2012 #2

    LCKurtz

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    Use row reduction.
     
  4. Oct 11, 2012 #3
    We haven't been taught that yet that's why I'm not sure what he wants us to do..

    We've been talking about linear independence, bases, and dimension but I don't know how I can go back and check if it spans the space.
     
  5. Oct 11, 2012 #4

    Zondrina

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    Have you been taught determinants? It would be much faster, but row reduction will give you the answer nicely.
     
  6. Oct 11, 2012 #5
    No, we haven't really been taught how to do anything with matrices, except maybe adding matrices or multiplying matrices by a scalar.
     
  7. Oct 11, 2012 #6

    Zondrina

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    Google row reduction. There's lots of stuff out there and it really only takes 20-30 mins to learn once you've seen a few examples done.

    EDIT : Here's a great explanation with an example :
     
    Last edited by a moderator: Sep 25, 2014
  8. Oct 11, 2012 #7
    Hmm, well, that helps, I think I can figure it out from here and I'll ask my professor if there was another method he expected us to know
     
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