Question: general solution

I initialise a matrix by recurrence, the dimension of the matrix and its elements depend on the (N1,N2) given. then, I create a vector of the same length of the matrix, its dimension is also defined by (N1,N2). then, I would like to linearsolve the matrix by the vector for a general solution with (N1,N2) as parameters. would this be possible?

here is the definition of the matrix and the vector:

-------------------------------------t: returns the position-----------------------------------------

------------------------------------InitM: return the matrix -----------------------------------------------

-----------------------------------------------------V: returns a vector----------------------------------------------

then, I linearsolve the matrix by the vector for my result

you can see that here, the whole program works only when N1 and N2 are given precisely. Is it possible that for N1 and N2 not given, (given as n1,n2), can I find the general result? the polynomial with n1 and n2, but not a paire of integer given. thanks a lot, if I have well explained my question.