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Homework Help: LU Matix decomposition problem with U.

  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]

    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 :(

    P.S. Why does my question look fine until i post it?? My matrixs look weird after posting!!
     
    Last edited: Jun 1, 2007
  2. jcsd
  3. Jun 1, 2007 #2
    ok i am really struggling to understand your working so i tried the question myself using the following row operations:
    R2' = R2 + (-1/2)R1
    R3' = R3 + (1/4)R1
    R3'' = R3' + (-1/2)R2

    the matrix was then reduced to triangular form:
    [4 2 6]
    [0 7 -1]
    [0 0 3]

    you can try to work out the determinants from here ...
    hope this helps
    Steven
     
  4. Jun 1, 2007 #3
    Got bored and decided to work it out ....

    just to confirm
    det(A)=det(U)
    As:
    det(U)=4(7x3)-2(0-0)+6(0-0)
    =4X21=84 as required

    Steven
     
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