Linear Algebra and Its Applications · Problem 2.5.7

Vector Spaces — Gilbert Strang

Mathematics · graphs-and-networks

Problem

If that second graph represents six games between four teams, and the score differences are

b_1, \ldots, b_6

, when is it possible to assign potentials

x_1, \ldots, x_4

so that the potential differences agree with the

b

's? You are finding (from Kirchhoff or from elimination) the conditions that make

Ax = b

solvable.