The Inspection Method for Nodal Analysis

In the inspection method the constants G₁₁, G₁₂, . . . , G_mm and I₁, I₂, . . . , I_m in the system of equations:

are obtained according to the following rules:

To get G_jj, where j = 1, 2, ... m (ie. the diagonal G 's), sum up the admittances of each of the branches attached to node j. (The admittance of a branch is the reciprocal of the impedance of that branch.)
To get I_j, where j = 1, 2, ... m (ie. the constants on the right-hand-side), find the value of v_s/R for each branch attached to node j and sum these values up. v_s is the voltage of the voltage source (if any) in that branch and R is the impedance in that branch. v_s is positive if the voltage source's polarity faces the node and is negative if it does not.
To get G_jk, where j is not equal to k (ie. the off-diagonal R 's), sum up the admittances of all the branches joining nodes j and k, and multiply this number by -1.