Wires go between Boston, Chicago, and Seattle. Those cities are at voltages
xB, xC, xS.
With unit resistances between cities, the three currents are in y:
y=Ax is ⎡⎣⎢yBCyCSyBS⎤⎦⎥=⎡⎣⎢101−1100−1−1⎤⎦⎥⎡ ⎣⎢xBxCxS⎤⎦⎥.
(a) Find the total currents
ATy
out of the three cities. (b) Verify that
(Ax)Ty
agrees with
xT(ATy)
six terms in both.