LU Matix decomposition problem with U.

[Chadlee88]

Homework Statement

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 have made the mistake.

Homework Equations

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]
[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!

 

[steven10137]

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

 

[steven10137]

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