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N times opeparations(lenear algebra)

  1. Feb 3, 2009 #1
    how to calculate the determinant of this:
    http://img6.imageshack.us/img6/4937/16190333pz1.gif

    b)
    solve this
    [​IMG]

    if it were a defined matrix i could sol it
    but there its "n" times

    ??
     
  2. jcsd
  3. Feb 11, 2009 #2
    i solved A
    how to solve B??
    i think of using cramer law
    but its an endless equation
    ??
     
  4. Feb 11, 2009 #3

    HallsofIvy

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    No, it's not an "endless" equation. For a given n, this is an n+1 by n+1 determinant equal to 0 so it is an nth degree polynomial equation.

    Have you tried it for n= 1, n= 2, etc.? You should be able to see a pattern pretty quickly. The roots are 0, 1, 2, ..., n-2.

    In fact it should be easy to see that if x= 0, the first two rows are exactly the same so the determinant is 0. If x= 1, the first and third rows are exactly the same. If x= 2, the first and fourth rows are exactly the same, etc.
     
    Last edited: Feb 11, 2009
  5. Feb 11, 2009 #4
    ok if i subtract the first row from the rest i get a diagonolized matrix
    |1 1 1 .. 1|
    |0 -x . . .. 1|
    |0 0 1-x 1|
    |0 0 0 .. n-2-x|

    -x(x-1)(x-2)...((n-2)-x)=0
    so the roots are from x=0 to x=n-2
    that correct??
     
  6. Feb 11, 2009 #5

    HallsofIvy

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    Yes, that is correct and a good way to solve it. (You shouldn't have the "1"s above the diagonal though.)
     
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