I'm a bit stuck. We're given the following system of equations: $$3x-2y+1=0$$ $$12x+3y-18=0$$
And they ask us whether Newton's Method converges after only one iteration. It's similar to this question I asked a few days ago Newton's Method for linearly dependent system of equations but here the two equations are not linearly dependent, so the Jacobian is invertible.
The Jacobian is $$\begin{bmatrix} 3 & -2 \\ 12 & 3 \end{bmatrix} $$ and its determinant is 33.
I'm a bit stuck about what to do next. I googled heavily but could not find an answer to my question.
Thanks for your help !