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A quick Pivot column question

  1. Apr 24, 2012 #1
    Matrix: Ã=
    1 -2 0 0 3
    2 -5 -3 -2 6
    0 5 15 10 0
    2 6 18 8 6

    Matrix on reduced echelon form:
    1 0 0 -2 3
    0 1 0 -1 0
    0 0 1 1 0
    0 0 0 0 0

    X 0 0 -2 3
    0 X 0 -1 0
    0 0 X 1 0
    0 0 0 0 0

    Are the pivot positions the ones I've marked with X? And therefor colum 1, 2 and 3 are pivot columns? Or have I completely misunderstood?



    Bonus question: Can't work out "Find a basis for Col(Ã), Row(Ã)". What does that even mean?
     
    Last edited: Apr 25, 2012
  2. jcsd
  3. Apr 25, 2012 #2
    Those are indeed the pivots.

    As for the bonus, the basis is just a set of linearly independent vectors that can represent every vector in a space.
     
    Last edited: Apr 25, 2012
  4. Apr 25, 2012 #3
    Great, thanks a lot.

    Linearly independent vectors? I've seen that before when I looked for the answer, but I didn't quite understand it. How do I check if it's linearly independent?
     
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