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.
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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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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