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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 69EQ

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Question

1. (a) Find the adjacency matrix of the following graph:
(c) Draw
5 5 5 5 5S
V3.
VA
V3
V2
U1
(b) Find the incidence matrix of the graph with vertex set {1, 22, 23, 24}
and edge set {1x2, 14, 223, 234, 24}.
the graph whose incidence matrix is:
V6
V5
1 1 1 0 00000
V2 10 0110000
0001 0 1 100
0000 1 1 010
0 1 0 0 0
V6 0 0 1 0 0
0
0 1 1
0
1 0 1

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Determine the adjacency matrix of the given graph.
Calculate the adjacency matrix for this graph
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SOLVE STEP BY STEP AND IN DIGITAL FORMAT 5. Draw the graph G that has as vertex set V (G) and edge set E(G) V (G) = (v1, v2, v3, v4, v5}, E(G) = {v1v2, v1v4, v1v5, v2v5, v2v3, v2v4}.
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III. Consider the directed graph described by the following:(a) Draw the graph.(b) Find a directed path from vertex 3 to vertex 6.(c) Find a directed cycle starting from and ending at vertex 4.(d) Find the adjacency matrix of the graph.(e) Does there exist a directed path from vertex 2 to vertex 6?
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