Question

利用克莱姆法则求解线性方程组{x1+x2-x3=-2, 2x1-x2+2x3=7, x1-x3=-1

Answer 1

解：
x1-2x2+3x3-4x4=4,
0+x2-x3+x4=-3,
x1+3x3+0+x4=1,
0-7x2+3x3+x4=-3

D=
1 -2 3 -4
0 1 -1 1
1 3 0 1
0 -7 3 1
=16

D1=
4 -2 3 -4
-3 1 -1 1
1 3 0 1
-3 -7 3 1
=-128

D2=
1 4 3 -4
0 -3 -1 1
1 1 0 1
0 -3 3 1
=48

D3=
1 -2 4 -4
0 1 -3 1
1 3 1 1
0 -7 -3 1
=96

D4=
1 -2 3 4
0 1 -1 -3
1 3 0 1
0 -7 3 -3
=0

所以x1=D1/D=-8
x2=D2/D=3
x3=D3/D=6
x4=D4/D=0