About LU factorization

[salvomic]

hi,
is seems that for LU in help there isn't anything.
LU gives permutation vector, Lower and Upper decomposition.

Having the matrix [[2,1,1], [4,-6,0], [-2,7,2]], after Linear Algebra books I should get L=[[1,0,0], [2,1,0], [-1,-1,1]] and U=[[2,1,1], [0,-8,-2], [0,0,1]]
in L under diagonal there are the "multipliers" (2, -1, -1: subtract 2 time row 1st from 2nd and so on), in U the diagonal items (2,-8,1) are the pivots.

In the Prime I get [1,3,2] (vector for permutation) and then
L=[[1,0,0], [-1,1,0], [2,-1,1]] and U=[[2,1,1], [0,8,3], [0,0,1]] (as the pivots would be 0, +8, 1, but the second should be -8).

I would like to understand why that difference showing the results...

thank you,
Salvo