How come fsolve fails to find a solution when the problem script returns the Jacobian (but works when no jacobian is returned) ?

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I am attempting to solve a system of nonlinear equations. My function script returns the Residual as well as the Jacobian with respect to the solution vector.
Fsolve is able to solve the equation when no Jacobian is returned (i.e only residual is returned) but fails when the jacobian is included. My jacobian is correct. I have compared it to numerically computed jacobian.
How is this possible? The error message says "the problem is locally singular". Which does not make sense since fsolve already solved it.

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