Answered: 2. Given a relation, R on A = {a, b, c,… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.4: Transistion Matrices And Similarity

Problem 15E

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2. Given a relation, R on A = {a, b, c, d} on as follows:
R = {(a, a), (a, b), (a, d), (b, b), (b, c), (c, c), (c, d), (d, a), (d, d)}
%3D
Show the matrix of relation, MR and determine whether the relation, R is an equivalence
relation.

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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?
Given A = {1,2, 3, 4} and B = {x,y , z}. Let R be the following relation from A to B:R = {(1,y),(1,z),(3,y),(4,x),(4,z)} Determine the matrix of the relation
Given the following matrix representation of a relation RR on the set A={a,b,c,d}A={a,b,c,d}, which of the following tuples is not in the relation?
Consider the matrix representing a relation R on the set {x, y, z}. 0 1 0 1 0 1 1 0 1 List the pairs in this relation, where row/column 1 corresponds to x, row/column 2 corresponds to y, and row/column 3 corresponds to z.
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
Let A = {2, 3, 4, 5, 6}, B = {11, 12, 13, 14, 15} and define the relation R from Ato B by aRb if a|b. Construct the matrix M corresponding to R.
Given that T is a relation on the set {1, 2, 3, 4}, and the set of ordered pairs is: T = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 3), (3, 2), (3, 3), (3, 4), (4, 1), (4, 3), (4, 4)}. Can you draw T as a directed graph? Can you show T as a matrix with elements that are zeros and ones? Is T reflexive? Can you explain why?
A. Write the relation on {a, b, c, d} in matrix form. 1. {(a, a), (a, d), (b, c), (c, d), (d, a), (d, c)} 2. {(a, c), (b, a), (b, d), (c, a), (c, d), (d, b), (d, d)}
Let A = {1, 2, 3, 4], B = {a, b, c}, C = {x, y, z}. Consider the relations R from A to B and S from B to C as follows: R = {(1, b), (3, a), (3, b), (4, c)} and S = {(a, y), (c, x), (a, z)} (i) Draw the diagrams of R and S. (ii) Find the matrix of each relation R, S (composition) RoS. (iii) Write R −1 and the composition RoS as sets of ordered pairs. (b) Find x and y where: (i) (x + 2, 4) = (5, 2x + y); (ii) (y − 2, 2x + 1) = (x − 1, y + 2)
Consider the relation R defined on the set X={a,b,c,d} and Y={1,2,3,4} from X to Y, where R={(?, 1); (?, 3); (?, 2); (?, 3); (?, 4); (?, 2)}.(i)Deduce the matrix of the complementary relation, ???, clearly outline and comment on your result.(ii) A relation T is defined on the set Y above from Y to Y as ? ={(1,1); (4,2); (1,3); (2,4); (2,1); (3,2); (3,3); (3,4); (1,2); (2,3); (4,4); (4,1)}, compute and analyze ????−1. (b) Given the functions f and g de defined by ?(?) =6?+57?−5, ? ≠57; ??? ?(?) = 2?2 − 3? + 4. Critically analyze and deduce the formula defining the (i) composition function gof (ii) inverse function ?−1(c)Apply the Runge-Kutta formula as a tool for solving and analyzing numerical differential equation, critically compute and analyze the numerical solution of ?′ = ?(?, ?) = 1 + ?2, y(0) = 0. Computing for the first step, with ℎ = 0.5
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.
Given, A = { 1,2,3,4 } , B = { x,y,z } Let R be the following relation from A to B: R = { (1,y),(1,z)(3,y)(4,x),(4,z) } Determine the matrix of the relation Draw the arrow diagram of R Find the inverse relation of R_1 of R

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