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Exercise 3.2.32

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$A^{T} y = 0$ :

y_{1} - y_{3} + y_{4} = - y_{1} + y_{2} + + y_{5} = - y_{2} + y_{4} + y_{6} = - y_{4} - y_{5} - y_{6} = 0 .

These equations add to $0 = 0$ . Free variables $y_{3}, y_{5}, y_{6} :$ watch for flows around loops.

The solutions to $A^{T} y = 0$ are combinations of $(- 1, 0, 0, 1, - 1, 0)$ and $(0, 0, - 1, - 1, 0, 1)$ and $(0, - 1, 0, 0, 1, - 1) .$ Those are flows around the 3 small loops.

mathchakra

2022-01-23 13:51

Exercise 3.2.32

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