Linear Algebra and Its Applications · Problem 2.5.2

Vector Spaces — Gilbert Strang

Mathematics · graphs-and-networks

Problem

For the same 3 by 3 matrix, show directly from the columns that every vector

b

in the column space will satisfy

b_1 + b_2 - b_3 = 0

. Derive the same thing from the three rows—the equations in the system

Ax = b

. What does that mean about potential differences around a loop?