Equivalent resistance, using node voltage analysis

1. The problem statement, all variables and given/known data


(I added in the R values for reference)

2. Relevant equations
GV=I
KCL

3. The attempt at a solution

I am not concerned with the MATLAB portion of the problem, only the setup.

I think what the problem wants me to do is:
1) connect a 1A test current from the ground source to v1 (like shown in the picture), find v1 using node voltage analysis, then find the equivalent resistance by dividing the test voltage (v1) by the test current, which is 1A.

2) connect a 1A test current from the ground source to v2. Repeat steps, where now v2 is the test voltage, to get equivalent resistance.

3) same as above, except with v4.

When I set up my system of equations I get too many unknowns.
For example, trying KCL on case 1 (where 1A is connected to v1), I get this system of equations:

v1/R1 + (v1-v2)/R2 + (v1-v3)/R6 = itest

(v2-v1)/R2 + (v2-v4)/R7 + (v2-v7)/R3 = 0

(v4-v2)/R7 + (v4-v3)/R11 + (v4-v6)/R12 = 0

Plugging in 1 for i and for all R values still gives me 6 different voltages to solve for, and only 3 equations.

Using the same method for case 2 and 3 (where vtest is v2 and v4 respectively), I get nearly identical systems of equations, the only difference being which equation is set equal to i instead of 0.

http://ift.tt/1gbcY2D

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