高斯消元法求矩阵的行列式

A=[1,-1,1,-4;5,-4,3,12;2,1,1,11;2,-1,7,-1]
Adet=1
%开始消元过程
for k=1:(length(A))
   a=A(k,k)
   Adet = Adet.*a
   for i=1:(length(A))
      A(k,i)=A(k,i)/a
   end
   for i=k+1:(length(A))
      c=-A(i,k)
	  for j=1: (length(A))
		A(i,j)=A(i,j)+c.*A(k,j)
	  end
   end
end
Adet

A =

     1    -1     1    -4
     5    -4     3    12
     2     1     1    11
     2    -1     7    -1


Adet =

     1


a =

     1


Adet =

     1


A =

     1    -1     1    -4
     5    -4     3    12
     2     1     1    11
     2    -1     7    -1


A =

     1    -1     1    -4
     5    -4     3    12
     2     1     1    11
     2    -1     7    -1


A =

     1    -1     1    -4
     5    -4     3    12
     2     1     1    11
     2    -1     7    -1


A =

     1    -1     1    -4
     5    -4     3    12
     2     1     1    11
     2    -1     7    -1


c =

    -5


A =

     1    -1     1    -4
     0    -4     3    12
     2     1     1    11
     2    -1     7    -1


A =

     1    -1     1    -4
     0     1     3    12
     2     1     1    11
     2    -1     7    -1


A =

     1    -1     1    -4
     0     1    -2    12
     2     1     1    11
     2    -1     7    -1


A =

     1    -1     1    -4
     0     1    -2    32
     2     1     1    11
     2    -1     7    -1


c =

    -2


A =

     1    -1     1    -4
     0     1    -2    32
     0     1     1    11
     2    -1     7    -1


A =

     1    -1     1    -4
     0     1    -2    32
     0     3     1    11
     2    -1     7    -1


A =

     1    -1     1    -4
     0     1    -2    32
     0     3    -1    11
     2    -1     7    -1


A =

     1    -1     1    -4
     0     1    -2    32
     0     3    -1    19
     2    -1     7    -1


c =

    -2


A =

     1    -1     1    -4
     0     1    -2    32
     0     3    -1    19
     0    -1     7    -1


A =

     1    -1     1    -4
     0     1    -2    32
     0     3    -1    19
     0     1     7    -1


A =

     1    -1     1    -4
     0     1    -2    32
     0     3    -1    19
     0     1     5    -1


A =

     1    -1     1    -4
     0     1    -2    32
     0     3    -1    19
     0     1     5     7


a =

     1


Adet =

     1


A =

     1    -1     1    -4
     0     1    -2    32
     0     3    -1    19
     0     1     5     7


A =

     1    -1     1    -4
     0     1    -2    32
     0     3    -1    19
     0     1     5     7


A =

     1    -1     1    -4
     0     1    -2    32
     0     3    -1    19
     0     1     5     7


A =

     1    -1     1    -4
     0     1    -2    32
     0     3    -1    19
     0     1     5     7


c =

    -3


A =

     1    -1     1    -4
     0     1    -2    32
     0     3    -1    19
     0     1     5     7


A =

     1    -1     1    -4
     0     1    -2    32
     0     0    -1    19
     0     1     5     7


A =

     1    -1     1    -4
     0     1    -2    32
     0     0     5    19
     0     1     5     7


A =

     1    -1     1    -4
     0     1    -2    32
     0     0     5   -77
     0     1     5     7


c =

    -1


A =

     1    -1     1    -4
     0     1    -2    32
     0     0     5   -77
     0     1     5     7


A =

     1    -1     1    -4
     0     1    -2    32
     0     0     5   -77
     0     0     5     7


A =

     1    -1     1    -4
     0     1    -2    32
     0     0     5   -77
     0     0     7     7


A =

     1    -1     1    -4
     0     1    -2    32
     0     0     5   -77
     0     0     7   -25


a =

     5


Adet =

     5


A =

     1    -1     1    -4
     0     1    -2    32
     0     0     5   -77
     0     0     7   -25


A =

     1    -1     1    -4
     0     1    -2    32
     0     0     5   -77
     0     0     7   -25


A =

     1    -1     1    -4
     0     1    -2    32
     0     0     1   -77
     0     0     7   -25


A =

    1.0000   -1.0000    1.0000   -4.0000
         0    1.0000   -2.0000   32.0000
         0         0    1.0000  -15.4000
         0         0    7.0000  -25.0000


c =

    -7


A =

    1.0000   -1.0000    1.0000   -4.0000
         0    1.0000   -2.0000   32.0000
         0         0    1.0000  -15.4000
         0         0    7.0000  -25.0000


A =

    1.0000   -1.0000    1.0000   -4.0000
         0    1.0000   -2.0000   32.0000
         0         0    1.0000  -15.4000
         0         0    7.0000  -25.0000


A =

    1.0000   -1.0000    1.0000   -4.0000
         0    1.0000   -2.0000   32.0000
         0         0    1.0000  -15.4000
         0         0         0  -25.0000


A =

    1.0000   -1.0000    1.0000   -4.0000
         0    1.0000   -2.0000   32.0000
         0         0    1.0000  -15.4000
         0         0         0   82.8000


a =

   82.8000


Adet =

   414


A =

    1.0000   -1.0000    1.0000   -4.0000
         0    1.0000   -2.0000   32.0000
         0         0    1.0000  -15.4000
         0         0         0   82.8000


A =

    1.0000   -1.0000    1.0000   -4.0000
         0    1.0000   -2.0000   32.0000
         0         0    1.0000  -15.4000
         0         0         0   82.8000


A =

    1.0000   -1.0000    1.0000   -4.0000
         0    1.0000   -2.0000   32.0000
         0         0    1.0000  -15.4000
         0         0         0   82.8000


A =

    1.0000   -1.0000    1.0000   -4.0000
         0    1.0000   -2.0000   32.0000
         0         0    1.0000  -15.4000
         0         0         0    1.0000


Adet =

   414