Finding my mistake reducing a 3x3 matrix to row echelon form

[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]

 

[Office_Shredder]

Divide the second row by 14, then subtract twice the second row from the first row. Figure out the rest from there

 

[daniel_i_l]

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.

 

[Chadlee88]

? 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 :(