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Describe which edges form loops in your graph. Use these to find a basis for the left nullspace of your graph. Does the system Az = b have solution(s) for the following choices of right-hand side vectors b? Justify your answer. 0 0 -------- (ii) b₂ = (i) b₁ = 2 3 (iii) b3 = 1 2 For any of the systems in the previous question, which of them have infinitely many solutions? Find a column vector representation of those solutions.

Describe which edges form loops in your graph. Use these to find a basis for the left nullspace of your graph. Does the system Az = b have solution(s) for the following choices of right-hand side vectors b? Justify your answer. 0 0 -------- (ii) b₂ = (i) b₁ = 2 3 (iii) b3 = 1 2 For any of the systems in the previous question, which of them have infinitely many solutions? Find a column vector representation of those solutions.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 16EQ
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A. Loops and Trees Draw a graph with numbered nodes and numbered, directed edges whose incidence matrix is A = (i) b₁ = -1 1 -1 0 0 0 1 0 01 0 -1 00 -1 1 1. Describe which edges form loops in your graph. Use these to find a basis for the left nullspace of your graph. (ii) b₂ = 2. Does the system Ar = b have solution(s) for the following choices of right-hand side vectors b? Justify your answer. (iii) b3 = 2 3. For any of the systems in the previous question, which of them have infinitely many solutions? Find a column vector representation of those solutions.
Transcribed Image Text:A. Loops and Trees Draw a graph with numbered nodes and numbered, directed edges whose incidence matrix is A = (i) b₁ = -1 1 -1 0 0 0 1 0 01 0 -1 00 -1 1 1. Describe which edges form loops in your graph. Use these to find a basis for the left nullspace of your graph. (ii) b₂ = 2. Does the system Ar = b have solution(s) for the following choices of right-hand side vectors b? Justify your answer. (iii) b3 = 2 3. For any of the systems in the previous question, which of them have infinitely many solutions? Find a column vector representation of those solutions.
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