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

Generally Newton's method says:
$x_{n+1} = x_{n} - \frac{f(x_n)}{f'(x_n)}$
In this case 
$f(\mathbf x) = A\mathbf x - b$
$\nabla f(\mathbf x) = A$
$\mathbf x_{1} = $$\mathbf x_{0} - \frac{A\mathbf x_0 - b}{A}\\
\mathbf x_{0} - \mathbf x_0 - A^{-1}b\\
A^{-1}b$
