Trying to solve 3 simultaneous equations, results seem erroneous

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])

Answer 1

[Jan]

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 = 

ans = 

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?

[Teshan Rezel]

Hi @Jan, thanks for replying. Indeed, I get the same result using both techniques but when I multiply out a into the equation, I get nothing but negative values! I'm not sure where the error might be on my part, given that the answers to the initial equations are themselves positive.

The purpose of doing this is to simulate the behaviour of the function across the limits of interest, although this may not be the best way of going about it, admittedly!

[Jan]

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]

Sorry @Jan, I think I've realised my error! You were correct, its the wrong methodology on my part!

Thanks!