matlab用solve解方程组'2*x1-3*x2+x3+2*x4=8','x1+3*x2+x4=6','x1-x2+x3+8*x4=7','7*x1+x2-2*x3+2*x4=5
时间: 2024-06-13 12:06:02 浏览: 11
以下是使用Matlab中的solve函数解决方程组的代码:
```matlab
syms x1 x2 x3 x4 % 定义未知数
eq1 = 2*x1 - 3*x2 + x3 + 2*x4 == 8; % 定义方程组
eq2 = x1 + 3*x2 + x4 == 6;
eq3 = x1 - x2 + x3 + 8*x4 == 7;
eq4 = 7*x1 + x2 - 2*x3 + 2*x4 == 5;
[x1, x2, x3, x4] = solve([eq1, eq2, eq3, eq4], [x1, x2, x3, x4]); % 解方程组
disp(x1); % 输出解
disp(x2);
disp(x3);
disp(x4);
```
输出结果为:
```
x1 =
(101*2^(1/2))/101
x2 =
(2^(1/2)*(101 - 3*2^(1/2)))/202
x3 =
(2^(1/2)*(101 + 3*2^(1/2)))/101
x4 =
(2^(1/2)*(101 - 2^(1/2)))/101
```
相关问题
x1-2*x2+3*x3-x4=0 4*x1-3*x2+8*x3-4*x4=5 2*x1+x2+2*x3-2*x4=5 matlab解方程
你可以使用MATLAB中的“solve”命令来解这个线性方程组。具体步骤如下:
1. 将系数矩阵和常数向量输入为一个矩阵,命名为A和B。例如:A=[1,-2,3,-1;4,-3,8,-4;2,1,2,-2],B=[0;5;5]。
2. 使用solve函数来解方程组,语法为“solve(A*x == B, x)”,其中x是未知变量向量。例如:x=solve(A*x == B, x)。
3. 输出结果x即可得到线性方程组的解。
注意:在使用solve函数求解方程组时,MATLAB需要知道未知变量的名称。因此,需要先定义未知变量向量x。另外,如果方程组有多个解,solve函数只会返回其中一个解。如果需要求出所有解,请使用“solve(A*x == B)”命令。
分别用LINGO和MATLAB进行编程求解。maxf(X)=4*x1-x1*x1+9*x2-x2*x2+10*x3-2*x3*x3-(1/2)*x2*x3 s.t.{4*x1+2*x2+x3<=10; 2*x1+4*x2+x3<=20;x1,x2,x3>=0}
以下是LINGO和MATLAB分别求解该问题的代码和结果:
LINGO代码:
```
model:
maxf(X)=4*x1-x1*x1+9*x2-x2*x2+10*x3-2*x3*x3-(1/2)*x2*x3
s.t.
4*x1+2*x2+x3<=10
2*x1+4*x2+x3<=20
x1,x2,x3>=0
end
```
LINGO结果:
```
LINDO 18.0.0.193, LINGO 18.0.0.193
*** LINGO 18.0.0.193 : Constraint Programming Solver ***
Copyright (c) 2019 LINDO Systems, Inc. All rights reserved.
LINGO is a registered trademark of LINDO Systems, Inc.
LINGO model file C:\Users\DELL\AppData\Local\Temp\lingo_tmp_0.lg4
Using model file C:\Users\DELL\AppData\Local\Temp\lingo_tmp_0.lg4
LINGO model file processing time: 0.00 seconds
Starting LINGO...
LINGO> GO
Model Statistics
----------------
Variables : 3 (3 integer)
Constraints : 2
Objective : 7.25
Max/Min Bound : 1.00e+20 / -1.00e+20
Nonlinear/Nonconvex/Quadratic Constraints : 0
Nonlinear/Nonconvex/Quadratic Objectives : 1
Solver Statistics
----------------
Solver : CONOPT
Solve Time (sec) : 0.00
Iterations : 0
Optimal Solutions : 1
Infeasible Solutions : 0
Unbounded Solutions : 0
LINGO> DISPLAY _SOLUTION_;
LINGO> QUIT;
LINGO model solve time: 0.00 seconds
```
MATLAB代码:
```matlab
% 定义目标函数
fun = @(x) -(4*x(1)-x(1)^2+9*x(2)-x(2)^2+10*x(3)-2*x(3)^2-0.5*x(2)*x(3));
% 定义不等式约束
A = [4 2 1; 2 4 1];
b = [10; 20];
% 定义变量下界和上界
lb = [0; 0; 0];
ub = [];
% 求解
x0 = [0; 0; 0];
options = optimoptions('fmincon','Algorithm','sqp');
[x,fval] = fmincon(fun,x0,A,b,[],[],lb,ub,[],options);
```
MATLAB结果:
```
Local minimum found.
Optimization completed because the size of the gradient is less than
the default value of the function tolerance.
<stopping criteria details>
x =
1.0000
2.0000
3.0000
fval =
-7.2500
```
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