Let V = {V₁, V2, V3} and R = {(V₁, V₁), (V₁, V2), (V₁, V3), (V2, V2), (V2, V3), (V3, V₁)}.a. Draw a directed graph to represent R and find MR.b. Find So, S₁, S2, and the shortest path matrix, S3.

Given the vertices , and the edge set .(a)The graph isHere, vertex 1 means v1, vertex 2 means v2,…

Let V = {V₁, V2, V3} and R = {(V₁, V1), (V₁, V2), (V1, V3), (V2, V2), (V2, V3), (V3, V1)}. a. Draw a directed graph to represent R and find MR. b. Find So, S1, S2, and the shortest path matrix, S3.

Let V = {V₁, V2, V3} and R = {(V₁, V1), (V₁, V2), (V1, V3), (V2, V2), (V2, V3), (V3, V1)}. a. Draw a directed graph to represent R and find MR. b. Find So, S1, S2, and the shortest path matrix, S3.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 70EQ

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Question

Let V = {V₁, V2, V3} and R = {(V₁, V₁), (V₁, V2), (V₁, V3), (V2, V2), (V2, V3), (V3, V₁)}.
a. Draw a directed graph to represent R and find MR.
b. Find So, S₁, S2, and the shortest path matrix, S3.

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Step 2: Finding the adjacency matrix of the graph

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Step 3: Finding S0 and S1

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Step 4: Finding S2 and S3

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