We will choose node 2 as the reference node and assign it a voltage of zero.
Write down Kirchoff's Current Law for each node. Call V1 the voltage at node 1,
V3 the voltage at node 3, V4 the voltage at node 4, and
remember that V2 = 0. The result is the following system of equations:
The first equation results from KCL applied at node 1, the second equation results from KCL applied
at node 3 and the third equation results from KCL applied at node 4. Collecting terms this becomes:
This form for the system of equations could have been gotten immediately by using the
Solving the system of equations using Gaussian elimination or some other method gives the