25. Use Algorithm 1 to find the transitive closures of these relations on {1, 2, 3, 4}. a) {(1, 2), (2, 1), (2, 3), (3, 4), (4, 1)}
25. Use Algorithm 1 to find the transitive closures of these relations on {1, 2, 3, 4}. a) {(1, 2), (2, 1), (2, 3), (3, 4), (4, 1)}
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CM: Cumulative Review
Problem 11CM
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Question
Hello. I am asking that all the work is shown on paper. I know the final answer is a 4 x 4 matrix containing all 1s. I'm just not getting that result. I have enclosed an example problem from the textbook that basically shows what I need to do. I'm having a hard time finding M2r, M3r, and M4r. Please show the work on how you get those. Help would be appreciated.
![THEOREM 3
Let MR be the zero-one matrix of the relation R on a set with n elements. Then the zero-one
matrix of the transitive closure R* is
MR* = MR V MR¹V MR¹v...v MR¹.
EXAMPLE 7 Find the zero-one matrix of the transitive closure of the relation R where
1 0 1
MR 01 0
0
=
Solution: By Theorem 3, it follows that the zero-one matrix of R* is
[3]
MR* = MR V MR¹V MR¹
Because
M²1
=
it follows that
MR*
=
and
MB1
10
0 1 0 0 1 0
=
0
9.4 Closures of Relations 603
V0 1 0 = 010
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5549ed10-80b3-43dd-a2ba-33df540a3cc8%2F348c3be7-bd88-4a09-b777-912fc666cff0%2Fne8xbwc_processed.png&w=3840&q=75)
Transcribed Image Text:THEOREM 3
Let MR be the zero-one matrix of the relation R on a set with n elements. Then the zero-one
matrix of the transitive closure R* is
MR* = MR V MR¹V MR¹v...v MR¹.
EXAMPLE 7 Find the zero-one matrix of the transitive closure of the relation R where
1 0 1
MR 01 0
0
=
Solution: By Theorem 3, it follows that the zero-one matrix of R* is
[3]
MR* = MR V MR¹V MR¹
Because
M²1
=
it follows that
MR*
=
and
MB1
10
0 1 0 0 1 0
=
0
9.4 Closures of Relations 603
V0 1 0 = 010
1
![25. Use Algorithm 1 to find the transitive closures of these
relations on {1, 2, 3, 4].
a) {(1, 2), (2, 1), (2, 3), (3, 4), (4,1)}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5549ed10-80b3-43dd-a2ba-33df540a3cc8%2F348c3be7-bd88-4a09-b777-912fc666cff0%2Fc384o4f_processed.png&w=3840&q=75)
Transcribed Image Text:25. Use Algorithm 1 to find the transitive closures of these
relations on {1, 2, 3, 4].
a) {(1, 2), (2, 1), (2, 3), (3, 4), (4,1)}
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