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4x4 determinant

  1. Jun 26, 2005 #1
    4x4 determinant(from my exam)

    a+b-- a--- a--- a
    a--- a+b-- a--- a
    a---- a-- a+b-- a detA=0
    a---- a--- a--- a+b

    How do I find a and b?
     
    Last edited: Jun 26, 2005
  2. jcsd
  3. Jun 26, 2005 #2

    matt grime

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    by finding the determinant and setting it equal to zero. do it by row operations
     
  4. Jun 26, 2005 #3

    Hurkyl

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    (note: this is a response to a deleted reply)

    How do you rearrange it like that with row and column swaps? (P.S. the determinant of the matrix you created is clearly zero, no matter what a and b are)
     
    Last edited: Jun 26, 2005
  5. Jun 26, 2005 #4
    yes you are right
     
  6. Jun 26, 2005 #5

    mathwonk

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    hurkyl, you have me puzzled as to why the determinant is clearly zero. take b = 1, a = 0 for instance. then the determinant sure looks like 1 to me, since the matrix is then the identity.

    therefore the set of (a,b) with det = 0 apparently forms a curve in the complex (a,b) plane.
     
  7. Jun 26, 2005 #6

    matt grime

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    i think hurkyl meant the rearranged one in qutzlcoatl's post, not the original one; i had to think about that too.
     
  8. Jun 26, 2005 #7

    mathwonk

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    oh, the deleted one.
     
  9. Jun 26, 2005 #8

    matt grime

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    yes, the now deleted one... at sciencefourms they don't let ordinary users do that for exactly this reason.
     
  10. Jun 26, 2005 #9
    sorry about that, i didn't want to leave something that was wrong and further confuse the matter. i leave it up next time.
     
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