load ex5-2-1
[m,l] = size(A);
B = [3 4 6];
N = setdiff(1:l,B);
[L,U] = lu(A(:,B));
x_B = U\(L\b)

x_B =

     1
     3
     5

u = L'\(U'\p(B))

u =

     0
    -3
     0

c = p(N)-A(:,N)'*u

c =

    -1
    -3
     3

s = 2;
d = U\(L\A(:,N(s)))

d =

     4
     6
    14

r = 1;
swap = B(r); B(r) = N(s); N(s) = swap;
[L,U] = lu(A(:,B));
x_B = U\(L\b)

x_B =

    0.2500
    1.5000
    1.5000

u = L'\(U'\p(B));
c = p(N)-A(:,N)'*u

c =

   -0.2500
    0.7500
    2.2500

s = 1;
d = U\(L\A(:,N(s)))

d =

    0.2500
   -0.5000
   -1.5000

r = 1;
swap = B(r); B(r) = N(s); N(s) = swap;
[L,U] = lu(A(:,B));
x_B = U\(L\b)

x_B =

     1
     2
     3

u = L'\(U'\p(B));
c = p(N)-A(:,N)'*u

c =

     1
     1
     2

diary off