PROBLEM 6 Part 1. Give the adjacency matrix for the graph G as pictured below: Figure 2: A graph shows 6 vertices and 9 edges. The vertices are 1, 2, 3, 4, 5, and 6, represented by circles. The edges between the vertices are represented by arrows, as follows: 4 to 3; 3 to 2; 2 to 1; I to 6; 6 to 2; 3 to 4; 4 to 5; 5 to 6; and a self loop on vertex 5. Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 × 5 matrix A is the adjacency matrix for G. The matrices A? and A are given below. 0 1 0 0 0 O 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 10 1 1 0 0 0 0 O o 1 0 0 O 0 0 0 10 0 0 1 10 1 1 1 0 10 A² = A³ = Use the information given to answer the questions about the graph G. (a) Which vertices can reach vertex 2 by a walk of length 3? (b) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A= A² A²)

PROBLEM 6 Part 1. Give the adjacency matrix for the graph G as pictured below: Figure 2: A graph shows 6 vertices and 9 edges. The vertices are 1, 2, 3, 4, 5, and 6, represented by circles. The edges between the vertices are represented by arrows, as follows: 4 to 3; 3 to 2; 2 to 1; I to 6; 6 to 2; 3 to 4; 4 to 5; 5 to 6; and a self loop on vertex 5. Part 2. A directed graph G has 5 vertices, numbered 1 through 5. The 5 × 5 matrix A is the adjacency matrix for G. The matrices A? and A are given below. 0 1 0 0 0 O 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 10 1 1 0 0 0 0 O o 1 0 0 O 0 0 0 10 0 0 1 10 1 1 1 0 10 A² = A³ = Use the information given to answer the questions about the graph G. (a) Which vertices can reach vertex 2 by a walk of length 3? (b) Is there a walk of length 4 from vertex 4 to vertex 5 in G? (Hint: A= A² A²)

Name: See attached, answer part 2 PROBLEM 6Part 1. Give the adjacency matrix
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Description: See attached, answer part 2 PROBLEM 6Part 1. Give the adjacency matrix for the graph G as pictured below:(236Figure 2: A graph shows 6 vertices and 9 edges. The vertices are 1, 2, 3, 4, 5, and6, represented by circles. The edges between the vertices

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 72EQ

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