Trying to solve 3 simultaneous equations, results seem erroneous

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Teshan Rezel 2021-6-1

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评论： Teshan Rezel 2021-6-2

Hi folks,

I am trying to solve the following set of equations. However, when plotting the results from the coefficients, I get all negative values when in reality, I'm expecting positive ones. Even the original equations have positive outcomes. Can you please advise on where I've gone wrong?

syms x y z
eqn1 = 109*x + 54*y + 124*z == 7.51;
eqn2 = 57*x + 30*y +63*z == 3.17;
eqn3 = 30*x + 17*y + 31*z == 1.24;
sol = solve([eqn1, eqn2, eqn3], [x, y, z]);
xSol = sol.x
ySol = sol.y
zSol = sol.z
a = 0:255;
ref = a*(xSol + ySol + zSol);
plot(ref)
xlim([0 255])

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Answer 1

Jan 2021-6-1

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https://ww2.mathworks.cn/matlabcentral/answers/845250-trying-to-solve-3-simultaneous-equations-results-seem-erroneous#answer_714345

编辑：Jan 2021-6-1

在 MATLAB Online 中打开

syms x y z

eqn1 = 109*x + 54*y + 124*z == 7.51;

eqn2 = 57*x + 30*y +63*z == 3.17;

eqn3 = 30*x + 17*y + 31*z == 1.24;

sol = solve([eqn1, eqn2, eqn3], [x, y, z]);

sol.x, sol.y, sol.z

ans =

This can be solved numerically also:

A = [109, 54, 124; 
      57, 30, 63; 
      30, 17, 31];
b = [7.51; 3.17; 1.24];
x = A \ b
%    [0.4529; -0.5380; -0.1033]

Of course, this is the same result.

So I assume, the only problem is:

ref = (0:255) * (xSol + ySol + zSol);

What is the purpose of adding the elements of the solution and multiplying it with a vector?

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Jan 2021-6-1

The result of A\b is a vector. I do not undestand why adding its elements and multiplying the result by 0:255 is meaningful. If xSol+ySol+zSol is negative, multiplying it with non-negative numbers must produce a non-negative result. In you case it is: -0.1884 * (0:255). How could this be positive?

Teshan Rezel 2021-6-2