A. Loops and Trees Draw a graph with numbered nodes and numbered, directed edges whose incidence matrix is A = -1 1 0 0 0 -1 0 0 0 1 1 0 0-1 -1 1

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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VIII. SESSION 9- GRAPHS AND NETWORKS
A. Loops and Trees
Draw a graph with numbered nodes and numbered, directed edges whose incidence matrix
is
(i) b₁ =
A =
1. Describe which edges form loops in your graph. Use these to find a basis for the left
nullspace of your graph.
2. Does the system Az = b have solution(s) for the following choices of right-hand side
vectors b? Justify your answer.
(ii) b₂ =
0
-1 1 0
-1 0 1
0
-1
0 0-1 1
0 1 0
워
(iii) b3 =
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:VIII. SESSION 9- GRAPHS AND NETWORKS A. Loops and Trees Draw a graph with numbered nodes and numbered, directed edges whose incidence matrix is (i) b₁ = A = 1. Describe which edges form loops in your graph. Use these to find a basis for the left nullspace of your graph. 2. Does the system Az = b have solution(s) for the following choices of right-hand side vectors b? Justify your answer. (ii) b₂ = 0 -1 1 0 -1 0 1 0 -1 0 0-1 1 0 1 0 워 (iii) b3 = 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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