Linear Algebra and Its Applications · Problem 2.5.12

Vector Spaces — Gilbert Strang

Mathematics · graphs-and-networks

Problem

If AA is a 12 by 7 incidence matrix from a connected graph, what is its rank? How many free variables are there in the solution to Ax=bAx = b? How many free variables are there in the solution to ATy=fA^T y = f? How many edges must be removed to leave a spanning tree?

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