Solving system of equations with 3 unknowns

Hello All,

I'm extracting points from a graph. I'll be using those points to find three unknowns from the equation of the form ax+by+cz = d.

If I'm extracting 3 points, then I can solve as simultaneous equations with 3 unknowns [AX=B form, Cramers's Rule]. But if I extract more than 3 points, how to solve?

Answer 1

[Matt J]

Whether with 3 or more than 3 variables, you will obtain an equation of the form

 A*X=B

and you would solve it by doing X=A\B. There is no need to use Cramer's rule (and it's probably not a good idea).

[Swasti Khuntia]

Thanks Matt for the reply. In my case, I've AX=B form, where

A = nx3 (known)

B = nx1 (known)

X = 3x1 (unknown)

I'm not getting any idea as how to find X.

Thanks again !!

[Matt J]

But I told you how to do it. You execute the operation.

X=A\B;

[Swasti Khuntia]

Thanks a lot. I found the solution using pinv function.

[Matt J]

No, it's a bad solution. X=A\B is much more efficient.

Answer 2

[Swasti Khuntia]

But in my case, pinv is the only solution.

[Matt J]

That would have to mean that you are not selecting enough linear independent points (2 or less). That raises the question as to why you don't just stop selecting after you have 2 points. That also raises the question as to how you hope to get a good fit to your parameters when you have fewer independent data points than parameters.