>> A=[-1 2 -1 3; 1 3 1 2; 0 1 3 1; 0 2 0 1]
A =

  -1   2  -1   3
   1   3   1   2
   0   1   3   1
   0   2   0   1

>> [L,U]=lu(A)
L =

   1.00000   0.00000   0.00000   0.00000
  -1.00000   1.00000   0.00000   0.00000
   0.00000   0.20000   1.00000   0.00000
   0.00000   0.40000   0.00000   1.00000

U =

  -1   2  -1   3
   0   5   0   5
   0   0   3   0
   0   0   0  -1

>> B=A([4 2 3 1],:)
B =

   0   2   0   1
   1   3   1   2
   0   1   3   1
  -1   2  -1   3

>> [LL,UU]=lu(B)
LL =

   0.00000   0.40000   0.00000   1.00000
   1.00000   0.00000   0.00000   0.00000
   0.00000   0.20000   1.00000   0.00000
  -1.00000   1.00000   0.00000   0.00000

UU =

   1   3   1   2
   0   5   0   5
   0   0   3   0
   0   0   0  -1

>> [LB,UB,PB]=lu(B)
LB =

   1.00000   0.00000   0.00000   0.00000
  -1.00000   1.00000   0.00000   0.00000
   0.00000   0.20000   1.00000   0.00000
   0.00000   0.40000   0.00000   1.00000

UB =

   1   3   1   2
   0   5   0   5
   0   0   3   0
   0   0   0  -1

PB =

   0   1   0   0
   0   0   0   1
   0   0   1   0
   1   0   0   0