Cut-set analysis of an electric network

Yes, good work. You used the "by inspection" method, but it doesn't lend itself to analysis automation. To find, then, the currents and voltages in each branch you have to proceed with the same method.  My work is an application of analysis based on fundamental cuts. In the case of "cut-set" analysis of a different circuit, it is sufficient to change the  cut-set matrix, the branch -impedance matrix and change the dimensions of the vectors and something else, obtaining voltages and currents in all the branches. Furthermore, I assumed that there are no mutual inductances. In this case everything becomes more complicated, even the analysis by inspection. For example, let's analyze the case in which there is a mutual inductance between two inductances.