I have a quick question. I have a system of residuals in the form of
$$R_i= (\sum_{j=1}^n a_{ij}x_j)-b_i$$
where $a_{ij}$ and $b_{i}$ are constants. I am trying to show that applying Newton-Raphson to this system of equations will converge to a solution in one iteration, independent of the initial guess. Does anyone have any ideas on demonstrating this?