Linear Algebra and Its Applications · Problem 2.5.11

Vector Spaces — Gilbert Strang

Mathematics · graphs-and-networks

Problem

With the last column removed from the preceding

A

, and with the numbers 1, 2, 2, 1 on the diagonal of

C

, write out the 7 by 7 system

C^{-1}y + Ax = 0, \quad A^T y = f.

Eliminating

y_1, y_2, y_3, y_4

leaves three equations

A^T C A x = -f

for

x_1, x_2, x_3

. Solve the equations when

f = (1,1,6)

. With those currents entering nodes 1, 2, 3 of the network, what are the potentials at the nodes and currents on the edges?