Assistance Needed: Solving System of Equations in MATLAB

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khadija 2024-1-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2070931-assistance-needed-solving-system-of-equations-in-matlab

评论： Sam Chak 2024-1-17

Certainly! Here's a message you can use to request help from the MATLAB community for solving the given system of equations:

Subject: Assistance Needed: Solving System of Equations in MATLAB

Dear MATLAB Community,

I hope this message finds you well. I am currently working on a project and find myself in need of some MATLAB expertise to solve a system of equations. The system consists of two equations:

Equation 1: 280 = -0.017*X - 0.496*Y + 0.341*Z - 7.076*E - 0.869*F - 0.772*U + 358

Equation 2: 1.5 = -0.004*X + 0.016*Y + 0.017*Z + 0.0221*E - 0.174*F + 0.11*U + 0.3

I would greatly appreciate it if someone from the community could provide me with a MATLAB command or script to solve for the variables X, Y, Z, E, F, and U in this system. Your assistance will be invaluable to my project.

Thank you in advance for your help!

Best regards,

Khadija

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Dyuman Joshi 2024-1-17

The system is underdetermined - You have 6 unknown variables and only 2 equations.

How do you expect to get a numerical solution for all the variables?

khadija 2024-1-17

OK i get it now . Thank you so Much

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Answer 1

Ninad 2024-1-17

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https://ww2.mathworks.cn/matlabcentral/answers/2070931-assistance-needed-solving-system-of-equations-in-matlab#answer_1391426

编辑：Ninad 2024-1-17

在 MATLAB Online 中打开

Hi Khadija,

As per my understanding you want to solve the given equation using MATLAB.

Equation 1: 280 = -0.017*X - 0.496*Y + 0.341*Z - 7.076*E - 0.869*F - 0.772*U + 358

Equation 2: 1.5 = -0.004*X + 0.016*Y + 0.017*Z + 0.0221*E - 0.174*F + 0.11*U + 0.3

However, there are more unknowns than there are equations, so there is no unique solution to the system.

For the given equations, it is only possible to express some of the variables in terms of the others, or you can find the solution to the equation by assigning values to 4 of the 6 variables used here.

You can use the MATLAB Symbolic Math Toolbox functions to solve the equation for two variables in terms of the other variables as follows:

% Define symbolic variables
syms X Y Z E F U
% Define the equations
eq1 = -0.017*X - 0.496*Y + 0.341*Z - 7.076*E - 0.869*F - 0.772*U == 280 - 358;
eq2 = -0.004*X + 0.016*Y + 0.017*Z + 0.0221*E - 0.174*F + 0.11*U == 1.5 - 0.3;
% Solve for two variables, for example, X and Y, in terms of the others
sol = solve([eq1, eq2], [X, Y], 'ReturnConditions', true);
% Display the solution
disp(sol.X);
disp(sol.Y);

You can refer the MATLAB documentation of "refer" function for better understanding:

https://in.mathworks.com/help/symbolic/sym.solve.html

Regards,

Ninad

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Sam Chak 2024-1-17

移动：Sam Chak 2024-1-17

在 MATLAB Online 中打开

Hi @khadija

Because the system is underdetermined, the 'solve' command returned some free parameters in which you can assign values arbitrarily to

to obtain X and Y.

% Declare the symbolic variables
syms X Y Z E F U
% The equations
eq1 = 280 == -0.017*X - 0.496*Y + 0.341*Z - 7.076*E - 0.869*F - 0.772*U + 358;
eq2 = 1.5 == -0.004*X + 0.016*Y + 0.017*Z + 0.0221*E - 0.174*F + 0.11*U + 0.3;
eqn = [eq1; eq2];   % group the equations
% The variables
var = [X, Y, Z, E, F, U];
% Solve the system
sol1= solve(eqn, var)
sol1 = struct with fields:
    X: 13600/47
    Y: 6925/47
    Z: 0
    E: 0
    F: 0
    U: 0
% Solve the system
sol2= solve(eqn, var, 'ReturnConditions', true)
sol2 = struct with fields:
             X: (2638*z2)/141 - (6263*z1)/141 - (21303*z)/470 + (868*z3)/141 + 13600/47
             Y: (1075*z3)/2256 - (259*z1)/1128 - (2479*z2)/1128 - (95599*z)/7520 + 6925/47
             Z: z3
             E: z
             F: z1
             U: z2
    parameters: [z    z1    z2    z3]
    conditions: symtrue