使用matlab求解方程组 如何用matlab求解齐次线性方程组
\u5982\u4f55\u7528matlab\u89e3\u65b9\u7a0b\u7ec4matlab\u4e2d\u89e3\u65b9\u7a0b\u7ec4\u8fd8\u662f\u5f88\u65b9\u4fbf\u7684\uff0c\u4f8b\u5982\uff0c\u5bf9\u4e8e\u4ee3\u6570\u65b9\u7a0b\u7ec4Ax=b(A\u4e3a\u7cfb\u6570\u77e9\u9635\uff0c\u975e\u5947\u5f02)\u7684\u6c42\u89e3\uff0cMATLAB\u4e2d\u6709\u4e24\u79cd\u65b9\u6cd5\uff1a
(1)x=inv(A)*b \u2014 \u91c7\u7528\u6c42\u9006\u8fd0\u7b97\u89e3\u65b9\u7a0b\u7ec4\uff1b
(2)x=A\B \u2014 \u91c7\u7528\u5de6\u9664\u8fd0\u7b97\u89e3\u65b9\u7a0b\u7ec4
PS\uff1a\u4f7f\u7528\u5de6\u9664\u7684\u8fd0\u7b97\u6548\u7387\u8981\u6bd4\u6c42\u9006\u77e9\u9635\u7684\u6548\u7387\u9ad8\u5f88\u591a~
\u4f8b:
x1+2x2=8
2x1+3x2=13
>>A=[1,2;2,3];b=[8;13];
>>x=inv(A)*b
x =
2.00
3.00
>>x=A\B
x =
2.00
3.00\uff1b
\u5373\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\u7ec4\u7684\u89e3x1\u548cx2\u5206\u522b\u662f2\u548c3\u3002
\u5bf9\u4e8e\u540c\u5b66\u95ee\u5230\u7684\u7528matlab\u89e3\u591a\u6b21\u7684\u65b9\u7a0b\u7ec4\uff0c\u6709\u7b26\u53f7\u89e3\u6cd5\uff0c\u65b9\u6cd5\u662f\uff1a\u5148\u89e3\u51fa\u7b26\u53f7\u89e3,\u7136\u540e\u7528vpa(F,n)\u6c42\u51fan\u4f4d\u6709\u6548\u6570\u5b57\u7684\u6570\u503c\u89e3.\u5177\u4f53\u6b65\u9aa4\u5982\u4e0b\uff1a
\u7b2c\u4e00\u6b65:\u5b9a\u4e49\u53d8\u91cfsyms x y z ;
\u7b2c\u4e8c\u6b65:\u6c42\u89e3[x,y,z,]=solve('eqn1','eqn2',,'eqnN','var1','var2','varN');
\u7b2c\u4e09\u6b65:\u6c42\u51fan\u4f4d\u6709\u6548\u6570\u5b57\u7684\u6570\u503c\u89e3x=vpa(x,n);y=vpa(y,n);z=vpa(z,n);\u3002
\u5982\uff1a\u89e3\u4e8c\uff08\u591a\uff09\u5143\u4e8c\uff08\u9ad8\uff09\u6b21\u65b9\u7a0b\u7ec4\uff1a
x^2+3*y+1=0
y^2+4*x+1=0
\u89e3\u6cd5\u5982\u4e0b\uff1a
>>syms x y;
>>[x,y]=solve('x^2+3*y+1=0','y^2+4*x+1=0');
>>x=vpa(x,4);
>>y=vpa(y,4);
\u7ed3\u679c\u662f\uff1a
x =
1.635+3.029*i
1.635-3.029*i
-.283
-2.987
y =
1.834-3.301*i
1.834+3.301*i
-.3600
-3.307\u3002
\u4e8c\u5143\u4e8c\u6b21\u65b9\u7a0b\u7ec4\uff0c\u51714\u4e2a\u5b9e\u6570\u6839\uff1b
\u89e3\u7b54\u5982\u4e0b\uff1a
\u57fa\u672c\u65b9\u6cd5\u662f\uff1asolve(s1,s2,\u2026,sn,v1,v2,\u2026,vn)\uff0c\u5373\u6c42\u8868\u8fbe\u5f0fs1,s2,\u2026,sn\u7ec4\u6210\u7684\u65b9\u7a0b\u7ec4\uff0c\u6c42\u89e3\u53d8\u91cf\u5206\u522bv1,v2,\u2026,vn\u3002
\u5177\u4f53\u4f8b\u5b50\u5982\u4e0b\uff1a
x^2 + x*y + y = 3
x^2 - 4*x + 3 = 0
\u89e3\u6cd5\uff1a
>> [x,y] = solve('x^2 + x*y + y = 3','x^2 - 4*x + 3 = 0')
\u8fd0\u884c\u7ed3\u679c\u4e3a
x =
1 3
y =
1 -3/2
\u5373x\u7b49\u4e8e1\u548c3\uff1by\u7b49\u4e8e1\u548c-1.5
\u6216
>>[x,y] = solve('x^2 + x*y + y = 3','x^2 - 4*x + 3= 0','x','y')
x =
1 3
y =
1 -3/2
\u7ed3\u679c\u4e00\u6837\uff0c\u4e8c\u5143\u4e8c\u65b9\u7a0b\u90fd\u662f4\u4e2a\u5b9e\u6839\u3002
\u901a\u8fc7\u8fd9\u4e09\u4e2a\u4f8b\u5b50\u53ef\u4ee5\u770b\u51fa\uff0c\u7528matlab\u89e3\u5404\u7c7b\u65b9\u7a0b\u7ec4\u90fd\u662f\u53ef\u4ee5\u7684\uff0c\u65b9\u6cd5\u4e5f\u6709\u591a\u79cd\uff0c\u53ea\u662f\u7528\u5230\u89e3\u65b9\u7a0b\u7ec4\u7684\u51fd\u6570\uff0c\u6ce8\u610f\u6b63\u786e\u4e66\u5199\u53c2\u6570\u5c31\u53ef\u4ee5\u4e86\uff0c\u975e\u5e38\u65b9\u4fbf\u3002
2\u3001\u53d8\u53c2\u6570\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u6c42\u89e3
\u5bf9\u4e8e\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u4e00\u822c\u7528fsolve\u547d\u4ee4\u5c31\u53ef\u4ee5\u4e86\uff0c\u4f46\u662f\u5bf9\u4e8e\u65b9\u7a0b\u7ec4\u4e2d\u67d0\u4e00\u7cfb\u6570\u662f\u53d8\u5316\u7684\uff0c\u8be5\u600e\u4e48\u6c42\u5462\uff1f
%\u5b9a\u4e49\u65b9\u7a0b\u7ec4\u5982\u4e0b\uff0c\u5176\u4e2dk\u4e3a\u53d8\u91cf
function F = myfun(x,k)
H=0.32;
Pc0=0.23;W=0.18;
F=[Pc0+H*(1+1.5*(x(1)/W-1)-0.5*(x(1)/W-1)^3)-x(2);
x(1)-k*sqrt(x(2))];
%\u6c42\u89e3\u8fc7\u7a0b
H=0.32;
Pc0=0.23;W=0.18;
x0 = [2*W; Pc0+2*H]; % \u53d6\u521d\u503c
options = optimset('Display','off');
k=0:0.01:1; % \u53d8\u91cf\u53d6\u503c\u8303\u56f4[0 1]
for i=1:1:length(k)
kk=k(i);
x = fsolve(@(x) myfun(x,kk), x0, options);%\u6c42\u89e3\u975e\u7ebf\u6027\u65b9\u7a0b\u7ec4
x1(i)=x(1);
x2(i)=x(2);
end
plot(k,x1,'-b',k,x2,'-r');
xlabel('k')
legend('x1','x2')
\u5148\u5199m\u6587\u4ef6
function [x,y]=line_solution(A,b)
[m,n]=size(A);
y=[];
if norm(b)>0
if rank(A)==rank([A,b])
if rank(A)==n
disp('\u65b9\u7a0b\u6709\u552f\u4e00\u89e3x');
x=A\b;
else
disp('\u65b9\u7a0b\u6709\u65e0\u7a77\u591a\u89e3,\u7279\u89e3\u4e3ax\uff0c\u5176\u9f50\u6b21\u65b9\u7a0b\u7ec4\u7684\u57fa\u7840\u89e3\u7cfb\u4e3ay');
x=A\b;
y=null(A,'r');%null\u662f\u7528\u6765\u6c42\u9f50\u6b21\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u57fa\u7840\u89e3\u7cfb\u7684\uff0c\u52a0\u4e0a'r'\u5219\u6c42\u51fa\u7684\u662f\u4e00\u7ec4\u6700\u5c0f\u6b63\u6574\u6570\u89e3\uff0c\u5982\u679c\u4e0d\u52a0\uff0c\u5219\u6c42\u51fa\u7684\u662f\u89e3\u7a7a\u95f4\u7684\u89c4\u8303\u6b63\u4ea4\u57fa\u3002
end
else
disp('\u65b9\u7a0b\u65e0\u89e3');
x=[];
end
else
disp('\u539f\u65b9\u7a0b\u7ec4\u6709\u552f\u4e00\u96f6\u89e3x');
x=zeros(n,1);
if rank(A)<n
disp('\u65b9\u7a0b\u7ec4\u6709\u65e0\u7a77\u4e2a\u89e3\uff0c\u57fa\u7840\u89e3\u7cfb\u4e3ay');
y=null(A,'r');
end
end
----------------------------------------------------------------------
\u4e3e\u4f8b\u8c03\u7528\uff1a
format rat %\u4ee5\u6709\u7406\u6570\u5f62\u5f0f\u8f93\u51fa
A=[1,1,-3,-1;3,-1,-3,4;1,5,-9,-8];
b=[1;4;0];
[x,y]=line_solution(A,b);
x,y
format short %\u4fdd\u75594\u4f4d\u6709\u6548\u6570\u5b57
使用matlab求解线性方程组，可以这样解。
首先，写出线性方程组的系数。即
A=[1 -9 -10;-9 1 -5;8 7 1];
其二，写出线性方程组的常数项系数。即
B=[1;0;4];
然后，用矩阵左除法，求出X=[x1,x2,x3] 的解。即
X=A\B
运行结果
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绛旓細涓銆鐢╩atlab 涓殑solve鍑芥暟 >>syms x y; %瀹氫箟涓や釜绗﹀彿鍙橀噺锛>>[x ,y]=solve('y=2*x+3','y=3*x-7');%瀹氫箟涓涓 2x1 鐨勬暟缁勶紝瀛樻斁x锛寉 >>x >>x=10.0000 >>y >>y=23.0000 浜屻傜敤matlab 涓殑鍙嶅悜鏂滅嚎杩愮畻绗︼紙backward slash锛夊垎鏋愶細鏂圭▼缁鍙寲涓 2*x-y=-3锛3*x-y...
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绛旓細syms x1 x2 x2=solve('sin(x1)=2*sin(x2)','x2');y=-0.15*cos(x1)+0.3*cos(x2)ezplot(y,[0 pi])
绛旓細1銆 鎵撳紑Matlab杞欢-->鐐瑰嚮鏂板缓鑴氭湰鑿滃崟锛屾柊寤轰竴涓剼鏈枃浠剁敤浜庣紪鍐欏井鍒鏂圭▼姹傝В绋嬪簭銆2銆 杈撳叆寰垎鏂圭▼姹傝В绋嬪簭-->鐐瑰嚮淇濆瓨-->鐐瑰嚮杩愯銆3銆佸湪matlab鐨勫懡浠ょ獥鍙ｅ嵆鍙湅鍒版眰瑙ｇ粨鏋滐紝鏄竴涓叧浜庡弬鏁癮锛宐鐨勮〃杈惧紡 绗簩绉嶆柟娉曪細鍒╃敤Matlab涓殑solver鍑芥暟(鍖呮嫭ode45銆乷de23銆乷de15s绛)鏉ユ眰瑙ｅ井鍒嗘柟绋嬬殑鏁板艰В...
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