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Draw a graph with numbered nodes and numbered, directed edges whose incidence matrix is (i) b₁ = 2 A: || 1700 (ii) b₂ = 0 -1 1 -1 0 1 1 0 0-1 1. Describe which edges form loops in your graph. Use these to find a basis for the left nullspace of your graph. 0 0 2. Does the system Ar= b have solution(s) for the following choices of right-hand side vectors b? Justify your answer. (iii) b3 = OOT- 1 0 -1 -2 0 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.

Draw a graph with numbered nodes and numbered, directed edges whose incidence matrix is (i) b₁ = 2 A: || 1700 (ii) b₂ = 0 -1 1 -1 0 1 1 0 0-1 1. Describe which edges form loops in your graph. Use these to find a basis for the left nullspace of your graph. 0 0 2. Does the system Ar= b have solution(s) for the following choices of right-hand side vectors b? Justify your answer. (iii) b3 = OOT- 1 0 -1 -2 0 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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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