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Matrix determinant problem

  1. Feb 14, 2008 #1
    1. The problem statement, all variables and given/known data
    I have to proove that the determinant of :

    x a a . . . a
    a x a . . . a
    . . .
    . . .
    a . . . a
    a . . . . . x

    If you get the idea (it's (n x n) with x's along the diagonal and a's everywhere else)

    That it is (x + (n-1)a)(x - a)^(n-1)


    I really don't have a clue how to do this so any hints appreciated.
     
  2. jcsd
  3. Feb 14, 2008 #2

    EnumaElish

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  4. Feb 14, 2008 #3

    HallsofIvy

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    Looks to me like induction on the size of the determinant would be best.

    If n= 1, the determinant is just (x + (1-1)a)(x - a)^(1-1)= x.

    Asume that formula is correct for a k by k determinant and evaluate the corresponding (k+1) by (k+1) determinant by expanding along the first row.
     
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