how to solve the following matrix in antenna array synthesis

hello sir/madam
plz find the attachment here. I need to to solve the equation -24. the perturbation(ε) values are required in my work. I hope all the necessary data is available with this attachment. If you require any further information i will send to you.Looking forward to your reply.
thank you sir/madam.

Hi,

Normally, you know the S and D matrix (D is derivative of S)... and N is the number of elements.
What are your unknowns that stop you ?

To solve your system, you could use Scilab (=Matlab free) ; it's just a suggestion.

BR

Thank you so much for your kind response sir.
In Equation--15 we have s(xm'). But we want s(xm) as per equation--22. can you give some suggestions regarding this. Can you plz differentiate between the terms εm and εn;; ζ (zeta) and xm, xn. Looking forward to your reply.

Actually we don't know how to find out 'S'.Is there any function available for finding derivatives in matlab?
Or do u suggest its better to use scilab for finding S and D?
Looking forward for ur reply sir.Thank you