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I am trying to solve systems of non-linear equations by hand using newtons method in preparation for an exam. Issue is that we have only used MatLab so far and no idea how to do this by hand. Specifically solving $J\delta = -F $ for $\delta$ where J is the Jacobian matrix and F is the solution to $F(U) = 0$.

So simply put, if I have $Ax = -b$, where $A$ is a matrix, $x$ and $b$ are vectors (and I only know A and b not x), how do I solve for $x$ given I will only have pen, paper and a regular scientific calculator?

e.g. In matlab I would do "-A\b" to use the mldivide function to get x.

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