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Row echelon form

  1. Jun 1, 2007 #1
    1. The problem statement, all variables and given/known data
    i'm trying to put the 3x3 matrix: [4 2 6]
    [ 2 8 2]
    [-1 3 1]
    into row echelow from.
    but i don't know where i'm goin wrong in my row operations. could some1 please tell me where i hav made the mistake.





    2. Relevant equations



    3. The attempt at a solution

    [4 2 6] [4 2 6 ] [4 2 6]
    [2 8 2] r2->r2+2r3 [0 14 4] r3-> 4r3 [0 14 4]
    [-1 3 1] [-1 3 1] [-4 12 4]


    r3->r3+r1 [4 2 6 ] r3->r3-r2 [4 2 6]
    [0 14 4] [0 14 4] :confused:
    [0 14 10 [0 0 6]
     
  2. jcsd
  3. Jun 1, 2007 #2

    Office_Shredder

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    Divide the second row by 14, then subtract twice the second row from the first row. Figure out the rest from there
     
  4. Jun 1, 2007 #3

    daniel_i_l

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    Gold Member

    What makes you think that that's wrong? With a few more operations you can get to I (the identity matrix) if that's what you need.
     
  5. Jun 1, 2007 #4
    ??? I'm trying to find the LU decomposition so U is jst an upper triangular matrix and that's what my answer above is. and from the fact that
    det(A) = det(LU) = det(L)det(U) = det(U) as det(L) = 1 the determinant of A has to be equal to the determinant of U. i worked out the determinant of A to be 84 but the determinant of U = 4((14x6)-(4x0))-2((0x6)-(4x0))+6((0x0)-(14x0)) = 4x14x6 = 336 which does not equal 84! i still dont' get what i've done wrong :(
     
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