Fourier transforms only work for a small percentage of functions CPL.Luke, so i'm not sure how transforming to the frequency domain would help you arrive at any equation in general. What did you have in mind?
if you change the values of the names you don't have to exclude any names as you can always make a system A X = B consistent by juggling the values of B. So i guess someone made the problem easier by doing that (but doesn't tell you how to assign the other letters as i cannot see a pattern there - if you can please enlighten me) , which leaves the original problem wide open. My money is still on finding the three physicists which don't fit (which fits into the general knowledge section of these uber IQ tests) and arriving at a 22 x 22 system which you can solve for integer values.
w=f[z], do you want my mathematica notebook?
Ok, first problem is that the system of linear equations is overdetermined and inconsistent as it stands in the question - so no programme will find a solution unless we somehow can eliminate the inconsistent equations. (The joys of mathematica - 7 lines of code and you have the matrix If anyone wants it just shout)
Now we need to work out which of the equations we can scrap and I'm guessing we need to scrap three of them to arrive at a unique solution. So i guess its a physics history lesson to work out which three physicists should not be on the list. I'm guessing its a theory, experiment division or something like that.
The catch here though is that when most people say "can you write down an equation for this graph" they usually mean "can you write down an equation using only finitely many additions, multiplications, exponents and compositions of elementary functions for this graph".
For this question the answer is sadly no, in fact almost all continuous graphs are not of that type.
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