Solution

lud=LUDecomposition[A]

[Graphics:1230f97.q2gr2.gif][Graphics:1230f97.q2gr1.gif]

[Graphics:1230f97.q2gr2.gif][Graphics:1230f97.q2gr3.gif]

Perm[v_]:=IdentityMatrix[Length[v]][[v]]

U=Upper[lud[[1]]]

L=Lower[lud[[1]]]

P=Perm[lud[[2]]]

P.L.U==A