Assistance Needed: Solving System of Equations in MATLAB

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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

[Dyuman Joshi]

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]

OK i get it now . Thank you so Much

Answer 1

[Ninad]

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

[khadija]

when i copy the command , Matlab don't give me any values of X and Y

"I am a beginner in matlab"

[Sam Chak]

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

[Ninad]

You won't get any absolute values for X and Y. The values of X and Y will be in terms of Z, E, F and U.

You are using 6 variables and 2 equations.

Either add 4 more equations or assign values to Z, E, F and U.

[khadija]

280=0,025*X-2,151*Y+247,72

1,7=-0,005*X+0,222*Y+4,472

And how about this equation

[Sam Chak]

@khadija, You already have the code above. Copy the equations into the code and show us the result.

Click this icon to copy & paste the code. Then click the Run button .