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Finding basis

  1. Oct 27, 2012 #1
    Let's say you have a 3x3 matrix and it's invertible. Let's call it A
    If you were to find a basis for the nullspace of A, would the basis just be the original 3 column vectors of A?
     
  2. jcsd
  3. Oct 27, 2012 #2

    Ray Vickson

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    What is the null space of an invertible matrix?

    RGV
     
  4. Oct 27, 2012 #3
    It would be the column vectors of A right?
     
  5. Oct 27, 2012 #4

    Dick

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    Ok, so you don't know what "invertible" means. Could you maybe look it up?
     
  6. Oct 27, 2012 #5
    det≠0 and a pivot is in every column for RREF(A).

    So for a 3x3 invertible matrix,it's basis is [1 0 0]^t [0 1 0]^t and [0 0 1]^t?
     
  7. Oct 27, 2012 #6

    Dick

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    That's an example of an invertible matrix. What vectors are in its null space?
     
  8. Oct 27, 2012 #7
    The 0 vector?
     
  9. Oct 27, 2012 #8

    Dick

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    Yes. Wouldn't that always be the only answer if A were invertible?
     
  10. Oct 27, 2012 #9
    I think I got it confused with the column space.
    A basis for the column space for this case would be the original 3 column vectors if A right?
     
  11. Oct 27, 2012 #10

    Dick

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    Sure. "column space" is different from "null space".
     
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