JACOBI method for a non-square matrix

I have to solve a linear system using an iterative method. I have to force residuals to zero.

The first matrix represents the partial derivatives of the saint venant equation, is the jacobian matrix, the second the correction and the last the residuals.

The final step is to compute the corrected values of the unknowns for the next iteration according to the following formulae

How can i solve this type of problem?

Thank you