discrete math Consider the relation described by the following digraph:Write the matrix of this relation. Use the matrix to determine if the relation is:a) reflexiveb) symmetricc) antisymmetricd) transitive

Consider the given digraph. We have to write the matrix of the given relation. Hence, the matrix of…

Answered: Consider the relation described by the…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 32CM: Prove that if A is similar to B and A is diagonalizable, then B is diagonalizable.

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Prove that if A is similar to B and A is diagonalizable, then B is diagonalizable.
Let A={a,b,c,d} and let R={(a,b)(b,c)(c,d)(d,b)} be a relation on A. Represent the relation using matrix
1. Create (a) the ordered pairs, (b) graphical representation, and (c) the relation matrix, for the Relation R ‘is a factor of’, on set B{1,2,3,6}. (d) Classify the relation R as reflexive, irreflexive, symmetric, antisymmetric, or transitive.
Let P={{a,b,d},{c,f},{e,g}} be a partition. Write the relation matrix for the implied equivalence relation.
Given the following relation, { ( A, A ), ( A, B ), ( A, E ), ( B, B ), ( B, E ), ( C, A ), ( C, B ), ( C, C ), ( C, D ), ( D, A ), ( D, B ), ( D, D ), ( E, C ), ( E, D ), ( E, E ) }i) Draw the digraph of the relation, ii) construct the matrix diagram for the relation, and iii) why or why not is the relation reflexive, symmetric, antisymmetric, transitive?
Determine whether the relations represented by these matrices are reflexive, irreflexive,symmetric, antisymmetric, and/or transitive. Justify each answer.
Make a list of pairs, construct the matrix, and draw the graph of the relation R from the set A = {0,1,2,3,4} to the set B = {0,1,2,3} suchthat (a, b) ∈ R if and only if a + b = 4.
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1. By using the attached graph of relation R1. a) Express R1 as a set of ordered pairs. b) create a matrix representation of R1. c) Determine if R1 is irreflexive, reflexive, symmetric, anti symmetric or transitive.
Write the relation matrix for the relation R on the set {a,b,c,d,e,f} which is defined as follows: R={(a,a), (a,b), (a,c), (b,a), (b,c), (c,a), (c,b), (d,d), (f,f)}.
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1. A) Write the ordered pairs, graphical representation, and the relation matrix, for the Relation R ‘is a factor of’, on set A{1,2,3,6}. B) determine if the relation R is reflexive, irreflexive, symmetric, antisymmetric, or transitive

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Consider the relation described by the following digraph: Write the matrix of this relation. Use the matrix to determine if the relation is: a) reflexive b) symmetric c) antisymmetric d) transitive