高斯消元法求矩阵的行列式
Posted 木卜
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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
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