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Often (most of the time??) the relevant system of equations is not linear in the unknowns.
Then, cannot decompose as Ax = b. Oh well.
Instead write as:
- f(x) = 0 function of one variable (1-D)
- f(x) = 0 x = (x1,x2,...,xn), f = (f1,f2,...,fn) (n-D)
Not guaranteed to have any real solutions, but generally do for astrophysical problems.