The vector x in your program has only three elements but the function newton/F requires a 5-element vector. If I correct this by setting x as 5-element vector with all 1's I get a singularity errror because the matrix created by F ist not invertible.
Hi! Hereafter, there are some examples that use the Newton algorithm. Lastly, there is also one related to your problem. But it is the only one that is not soluble in the presence of a singularity.
