matlab求解带参数方程组 MATLAB求解带有字母参数的方程组如何计算
matlab\u6c42\u89e3\u5e26\u53c2\u6570\u65b9\u7a0b\u7ec4matlab\u4e2d\u7684solve\u51fd\u6570\u4e0d\u4f46\u80fd\u89e3\u76f4\u63a5\u6c42\u89e3\uff0c\u8fd8\u80fd\u6c42\u89e3\u5e26\u53c2\u6570\u7684\u65b9\u7a0b\uff1a
clear
all
syms
r
x
a
b
c
d
x1
x2
x3
x4;
[x1,x2,x3,x4]=solve('r*x1+r*x3-x*x4=a','r*x2+x*x3+r*x4=b','r*x1-x*x2+r*x3=c','x*x1+r*x2+r*x4=d','x1,x2,x3,x4')
\u6211\u8fd0\u884c\u4e86\u4e00\u4e0b\u7ed3\u679c\u5982\u4e0b\uff1ax1
=
(2*r^2*d-2*r^2*b+r*x*c+r*a*x+x^2*d)/x/(4*r^2+x^2)
x2
=
(-2*r^2*c+x*r*d+r*x*b-x^2*c+2*r^2*a)/x/(4*r^2+x^2)
x3
=
1/x*(-2*r^2*d+2*r^2*b+r*x*c+x^2*b+r*a*x)/(4*r^2+x^2)
x4
=
-(-2*r^2*c-x*r*d-r*x*b+2*r^2*a+x^2*a)/x/(4*r^2+x^2)
>>
\u4f60\u53ef\u4ee5\u5c06y2=2\u4e5f\u4f5c\u4e3a\u65b9\u7a0b\u5e26\u8fdb\u53bb\uff1a
S = solve('x1+y2*y1=5', '3*x1-y1=7', 'y2=2');S.x1S.y1\u5982\u679c\u60f3\u8981\u6d6e\u70b9\u6570\u7ed3\u679c\u7684\u8bdd\uff1a
vpa(S.x1)vpa(S.y1)
[ R 0 R -X][x1]=[a]
[ 0 R X R][x2]=[b]
[ R -X R 0][x3]=[c]
[ X R 0 R][x4]=[d]
要解的是[x1 x2 x3 x4]'('表示转秩)矩阵，这个矩阵等于
[ R 0 R -X]
[ 0 R X R]
[ R -X R 0]
[ X R 0 R]
的逆阵乘以[a b c d]'
matlab的话，就求上面4x4矩阵的逆就行，即矩阵的-1次方，然后再乘以[a b c d]'，得到一个4x1矩阵就是[x1 x2 x3 x4]'。
如果系数没有逆阵，说明该方程不完备，无解
MATLAB中的SOLVE函数不但能解直接求解，还能求解带参数的方程：
clear all
syms R X a b c d x1 x2 x3 x4;
[x1,x2,x3,x4]=solve('R*x1+R*x3-X*x4=a','R*x2+X*x3+R*x4=b','R*x1-X*x2+R*x3=c','X*x1+R*x2+R*x4=d','x1,x2,x3,x4')
我运行了一下结果如下：x1 =
(2*R^2*d-2*R^2*b+R*X*c+R*a*X+X^2*d)/X/(4*R^2+X^2)
x2 =
(-2*R^2*c+X*R*d+R*X*b-X^2*c+2*R^2*a)/X/(4*R^2+X^2)
x3 =
1/X*(-2*R^2*d+2*R^2*b+R*X*c+X^2*b+R*a*X)/(4*R^2+X^2)
x4 =
-(-2*R^2*c-X*R*d-R*X*b+2*R^2*a+X^2*a)/X/(4*R^2+X^2)
>>
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