Newton's Method for nonlinear systems What does Newton’s Method for nonlinear
systems reduce to for the linear system Ax = b
where A is a nonsingular matrix?
Like what is the corresponding multivariate function and Jacobian of the System?
Having a hard time with the abstract form

If $f(x):=b-Ax$, 
$$
\nabla f(x)=-A,
$$
so if $x_0$ is an initial guess of the Newton method, the update
$$
x_1=x_0-[\nabla f(x_0)]^{-1}f(x_0)
$$
boils down to
$$
x_1=x_0+A^{-1}(b-Ax_0)=A^{-1}b.
$$
