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Determinant of matrix

  1. Sep 19, 2009 #1
    How can I get the determinant of this matrix?

    1-n 1 ....1 1
    1 1-n ...1 1
    . . . .
    . . . .
    1 1 .... 1 1-n

    I think that the answer is 0 but... why?

    Thank you.
     
  2. jcsd
  3. Sep 19, 2009 #2

    HallsofIvy

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    Is "n" here the order of the matrix? If so then, by a row reduction to diagonal or triangular form, you can show that the last row becomes all "0"s.
     
    Last edited: Sep 19, 2009
  4. Sep 19, 2009 #3
    Thx for your reply, but I can't see how u get to this solution.. Can u show me the process?
    Thanks again!
     
  5. Sep 19, 2009 #4

    HallsofIvy

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    Try this: add all of the other rows to the first row. What do you get?

    (Try it with n= 2, 3, and 4 first.)
     
  6. Sep 19, 2009 #5
    Alright, so, if I have a determinant with n=4, i add all the rows to the first and i get (4-n +4-n +4-n +4-n), so, it's 0.

    Is there any other process?

    Thank you.
     
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