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SunnySkyguy: Sorry, I don't quite understand what you mean.
Could you be more specific?
Ratch:
That paragraph really explains why. However, there is still a probem that is still confusing.
In proving sum of the elements in each column is zero, why can we set all terminal voltages except the kth one to zero?
I think that is because Y matrix is constant and independent to terminal voltages and currents. So, I can set terminal voltages to whatever I want.
Not shown in the 3 terminal schematic is the common ground path. ( which can be any arbitrary potential)
When you look at a 1 port scenario, I1=Y11*V1 , is a variation of Ohm's Law I=V/R where R= 1/Y11
When you look at the 2 port matrix, it becomes Kirchoff's Current Law.
The sum of the matrix network currents is zero.
... based on KCL law ...
The algebraic sum of currents in a network of conductors meeting at a point is zero.
Node values are interactive with the admittance of each port, but there must be at least one driving force, either an ideal voltage source ( which might be represent as a practical source with some admittance)
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