Let A = {1,2,3,4} and R and S be two relations on A whose matrices are ´1 0 0 1] [1 0 0 1] 1 0 0 1 0 0 1 0 [1 0 0 1] 0 1 0 0 1 0 1 Ms = 1 MR = 1 0 0 1. Find A) The complementary relation of R B) Ro S C) Transitive closure of R D) Symmetric closure of S

Let A = {1,2,3,4} and R and S be two relations on A whose matrices are ´1 0 0 1] [1 0 0 1] 1 0 0 1 0 0 1 0 [1 0 0 1] 0 1 0 0 1 0 1 Ms = 1 MR = 1 0 0 1. Find A) The complementary relation of R B) Ro S C) Transitive closure of R D) Symmetric closure of S

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 44EQ

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Question

Let A = {1,2,3,4} and R and S be two relations on A whose matrices are
´1 0 0 1]
[1 0 0 1]
1 0 0 1
0 0 1 0
[1 0 0 1]
0 1 0
0 1 0
1
Ms =
1
MR =
1 0 0 1.
Find
A) The complementary relation of R
B) Ro S
C) Transitive closure of R
D) Symmetric closure of S

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