第3章-线性方程组(3)

from sympy.matrices import *
from sympy import symbols,Eq,solve

1.多阶方程组
a11,a12,a13,a14=symbols('a11 a12 a13 a14')
a21,a22,a23,a24=symbols('a21 a22 a23 a24')
a31,a32,a33,a34=symbols('a31 a32 a33 a34')
a41,a42,a43,a44=symbols('a41 a42 a43 a44')
x1,x2,x3,x4=symbols('x1 x2 x3 x4')
b1,b2,b3,b4=symbols('b1 b2 b3 b4')
f1=Eq(a11*x1+a12*x2+a13*x3+a14*x4,b1)
f2=Eq(a21*x1+a22*x2+a23*x3+a24*x4,b2)
f3=Eq(a31*x1+a32*x2+a33*x3+a34*x4,b3)
f4=Eq(a41*x1+a42*x2+a43*x3+a44*x4,b4) 
solve([f1,f2,f3,f4],[x1,x2,x3,x4])

结果:

2.二阶方程组
f1=Eq(a11*x1+a12*x2,b1)
f2=Eq(a21*x1+a22*x2,b2)
solve([f1,f2],[x1,x2])

2. 求方程组解
from sympy.matrices import *
from sympy import symbols,Eq,solve
x1,x2,x3,x4=symbols('x1 x2 x3 x4')
f1=2*x1+x2-5*x3+x4-8
f2=x1-3*x2-6*x4-9
f3=2*x2-x3+2*x4+5
f4=x1+4*x2-7*x3+6*x4
fm=solve([f1,f2,f3,f4],[x1,x2,x3,x4])
fm

或者

x1,x2,x3,x4=symbols('x1 x2 x3 x4')
f1=Eq(2*x1+x2-5*x3+x4,8)
f2=Eq(x1-3*x2-6*x4,9)
f3=Eq(2*x2-x3+2*x4,-5)
f4=Eq(x1+4*x2-7*x3+6*x4,0)
fm=solve([f1,f2,f3,f4],[x1,x2,x3,x4])
fm