(adsbygoogle = window.adsbygoogle || []).push({}); 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]

[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!!

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# Homework Help: LU Matix decomposition problem with U.

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