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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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Let G be an undirected graph, with adjacency matrix
1 0
1 0
1
1
1
A =
1
1
1
1
1
1
1
1
1 0
How many walks of length 3 does G posses from vertex 2 to vertex 4?
You may use the following results:
2
1
2
1
1
1
3
1
2
2
A? =
1
3
2
1
%3D
1
2
4
1
1
2
1
1
2
5
3
6.
3
5
4
7
7 3
A³ :
3
7
4
7
5
7
7
6.
3
3
5
6 2
Answer:
2.

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