Let A = {1,2,3,4} and R a relation on A whose matrix [1 0 1 1 0 1 is MR 1 0 1 1 1 1 1 Determine which of the following properties are satisfied on R: reflexive, irreflexive, symmetric, asymmetric, antisymmetric, transitive. ( Show your work)

Let A = {1,2,3,4} and R a relation on A whose matrix [1 0 1 1 0 1 is MR 1 0 1 1 1 1 1 Determine which of the following properties are satisfied on R: reflexive, irreflexive, symmetric, asymmetric, antisymmetric, transitive. ( Show your work)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Linear Transformations

Section6.2: The Kernewl And Range Of A Linear Transformation

Problem 63E

See similar textbooks

Related questions

Q: 9*) Let J and K be the Jacobian matrices of the functions y; = f:(x1, 82,. and their inverse…

A: Given: J & K are the Jacobian matrices of the functions yi=fi(x1,x2,....,xn) &…

Q: Let R, and R2 be relations on a set A represented by the matrices 1 01 [1 1 0] 1 0 Lo 1 0J [1 = 0 1…

Q: 5) Prove that the map T : R³ → R³ defined by T((x1, x2, x3)) = (2x1 – 3x2 + 8x3, 4x2 – x3, 2x1) - is…

Q: Q4. Let A = { 1, 2, 3, 4, 5, 6} and relation R on A defined by R = { (x,y)|(x+y) is a divisor of 24…

A: A=1,2,3,4,5,6 and relation R on A defined by R=x,y| x+y is a divisor of 24 So,…

Q: Which of the following matrices shows that (3, 2) belongs to the relation it represents? (Select all…

Q: Let A = {p, q, r, s} and the relation R on A is represented by the matrix (0 0 1 1) 0 1 0 0 . Find…

Q: Let Pn be the vector space of all polynomials of degree n or less in the variable x. Let D : P3 → P2…

Q: Let R1 and R2 be relations on a set represented by the matrices. 0. 0. 1 MR. 1 1) and Mg, 1 1 1 1 1…

A: given let R1 and R2 be relations on a setMR1=010111100andMR2=010011111R1 o R1 =(a,c)|(a,b)…

Q: 4. Let f1, f2, fz be functions in F(R). a. For a set of real numbers x1, X2, X3, let (F(x;)) be the…

A: Assume the functions f1,f2,f3 have first and second derivatives on some interval a,b and let Wx is…

Q: A, BE R"Xn 2. Let n EN. Consider the following binary relation for A-B : 3Q E R"*": Q. A A= QB…

Q: Given the function L : P2 → P2 given by L(p(t)) = tp'(t). (a) By definition, show that L is a linear…

A: (a) Let P2 is a set of all polynomial of degree at most 2. Let L:P2→P2 given by Lp(t)=tp't. Let…

Q: If the transitive closure R* of the zero-one matrix MR is Mg = MR V M v M v MI Find the zero-one…

A: Given zero one matrix MR is MR=0100001001001000 Also, Transitive closure R* of the zero one matrix…

Q: Let R1 and R2 be the relations represented in the matrix. [0 1 0 1] [1 0 1 1] 0010 0010 R2 1 100 1 1…

Q: ,Let Pn be the vector space of all polynomials of degree n or less in the variable r. Let D : P3 →…

Q: Which of the following is true for matrix A 1 00 0 100 2 010-2 00 1 Minimal polynomial of A is x' +…

A: To find which of the following is true about matrix A .

Q: 4. Let f1, f2, fz be functions in F(R). For a set of real numbers x1, x2, X3, let (f(x,)) be the…

A: Note:- Here, you don't mention field TR is ℝ or anything else. So, i'm assuming this ℝ. If it is…

Q: VII.3. Let Rbe the relation on {1, 2, 3, 4} given by r Ry if, and only if, æ – y = 0. Represent Rin…

Q: Let L be the operator on P3 defined byL (p(x)) = xp'(x) + p''(x) Find the matrix A representing L…

A: L (p(x)) = xp'(x) + p''(x) We have to find the matrix A representing L with respect to [1, x, x2].

Q: Consider the relation R on set A = {1,2, 3, 4, 5, 6, 7, 8, 9} with the 0-1 matrix representation: [o…

A: According to our guidelines we will be answering the first part of your question. If you want the…

Q: Let a €R and consider the transformation T : R' → R³ defined by T(r1, 12, T3, x4)) = (ax1 + 5x2 +…

Q: Let Pn be the vector space of all polynomials of degree n or less in the variable x. Let D : P3 → P2…

Q: Let L be the operator on P3 defined byL (p(x)) = xp'(x) + p''(x) Find the matrix B representing L…

Q: Let U be a unitary matrix. Prove that ||Ux|| = ||x|| for all x ∈ Cn.

Q: 15. Show that T is a linear transformation from R4 to R4 by finding a matrix that implements the…

Q: a. If R is a relation defined from the Set A = { 6,12,25,36} to the set B = {3,4,5,6} as follows: R…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: Let L be the linear operator on R³ defined by 2x1 – x2 – X3 L(x) = | 2x2 – x1 – X3 2x3 – X1 – X2…

Q: Let P, be the vector space of all polynomials of degree n or less in the variable x. Let D : P3 → P2…

Q: 3. Define a mapping T: P3-P3 by. T(f(x))=f(x) Please find the nullity of T. (Hint: Still dx by using…

Q: Let X be a set of 2×3 matrices. if for any a1 az az A = B = b1 b2 b3 b4 b5 b6 EX, a4 a5 a6 6 d(A, B)…

Q: Let A = {a, b, c, d} and let R and S be the relations on A whose matrices are (1 0 1 0` 0 1 0 1 (1 0…

A: let A=a,b,c,d and let R and S be the relations on A whose matrices are MR=1010010110100101 and…

Q: 2. Suppose that T : R³ → R² is defined by T(x1, x2, x3)= (x1 – x2, x2 – 13). (a) Find the standard…

A: NOTE: Hi! Thank you for your question. As per the honor code we are allowed to answer three sub…

Q: Find the matrix of the transitive closure

A: Note: Here you have posted two different matrices. we are taking the first matrix. For the second…

Q: Find all x in R* that are mapped into the zero vector by the transformation x-Ax for the given…

A: Answer is : X = (0 0 0 0) t

Q: Let A = {p, q, r, s} and the relation R on A is represented by the matrix 0 0 1 1 c) 0 1 0 0 MR .…

A: As per the guidelines, I am supposed to do the first problem only. Kindly pst the other question…

Q: Let B be an n ×n invertible matrix. Define Φ: Mn×n(F) →Mn×n(F) by Φ(A) = B−1AB. Prove that Φ is an…

Q: :Prove that the function f(x₁, x,)=- X₂ X₂ purpose, compute the Hessian matrix for f(x). defined on…

A: The given function is f(x1,x2)=1x1x2 defined on the domain ℝ++2. The objective is to prove that…

Q: Let T be the triangle with vertices (x₁, y₁). (x2. y2), and (X3, 3), and let a с b d Let f be the…

A: Given, T be a triangle with vertices x1,y1,x2,y2, and x3,y3. f is the matrix transformation defined…

Q: [1 1 0 1 011 (a) Let MR = 1 . The relation represented by the matrix MR is 0 1 1 0 1 1. i.…

Q: [o 1 0 1 10 1 1 0 10 0 11 0 0 13. Let A = {1, 2, 3, 4} and matrix of relation R is Mg= Determine if…

Q: Let E be any bounded closed set in the complex plane containing an infinite number of points, and…

Q: Let Pn denote the vector space of polynomials in the variable x of degree n or less with real…

Q: Let A = {1,2,3, 4} and R a relations on A whose matrices is 1. 1 1 1 1 1 1 MR = |0 0 0 1 1 1 1 0 0 0…

Q: 4. Let f1, f2, f3 be functions in F(R). a. For a set of real numbers x1, X2, X3, let (f(x;)) be the…

A: Given - f1x = e-x , f2x = x, f3x = e2x To show - Show that the following set of functions are…

Q: For each of the following linear transformationsL mapping R3 into R2, find a matrix A such thatL (x)…

Q: Let R be a relation on A = {1,2,3,4} such that aRb means |a – b| < 1. Find the matrix…

Q: Given the following matrix representation of a relation R on the set A = {a, b, c, d}, which of the…

Q: Let Pn be the vector space of all polynomials of degree n or less in the variable x. Let D : P3 → P2…

A: We will solve this problem in some steps

Q: 6. Find a basis for the null space of the functional f defined on R³ by ƒ(x) = §1 +§2 − §3, where x…

Q: Let R[r], be a linear space with all polynomials p(x) = az²+bx+c (a,b,c ER) whose degree is no more…

A: We have to find the matrix A representing L with respect to the given basis. Then we can proceed…

Q: matrix of the transitive closure

A: We have to find find out the matrix of the transitive closure of R. It is given that…

Question

Let A = {1,2, 3, 4} and R a relation on A whose matrix
1]
[1 0
1
0 0
is Mr =
1
1
1
1
1
1
1
Determine which of the following properties are satisfied on
R: reflexive, irreflexive, symmetric, asymmetric, antisymmetric,
transitive. ( Show your work)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Relations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Prove statement d of Theorem 3.9: If G is abelian, (xy)n=xnyn for all integers n.
Complete the proof of Theorem 5.30 by providing the following statements, where and are arbitrary elements of and ordered integral domain. If and, then. One and only one of the following statements is true: . Theorem 5.30 Properties of Suppose that is an ordered integral domain. The relation has the following properties, whereand are arbitrary elements of. If then. If and then. If and then. One and only one of the following statements is true: .
6. In Example 3 of section 3.1, find elements and of such that but . From Example 3 of section 3.1: and is a set of bijective functions defined on .
Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
Suppose that A is an invertible matrix over and O is a zero matrix. Prove that if AX=O, then X=O.
Let T be a linear transformation from P2 into P2 such that T(1)=x,T(x)=1+xandT(x2)=1+x+x2. Find T(26x+x2).
b) Check whether the relation R on the set S = {1, 2, 3} with the the matrix 1 1 1 0 1 1 1 1 1 is an equivalence relation. Which of the following properties R has: reflexive, symmetric, anti-symmetric, transitive? Justify your answer in each case?
Let R be a relation on the set A = {a, b, c, d} described by the matrixMR=(1 0 0 1 0 1 0 1 0 1 0 0 0 1 0 0) Find the domain and range of R and Find R(a) and R({c, d}).
A. Let R be a relation on set A. A={x : x ∊ J and 0 ≤ x ≤ 12}, and R={(a,b) : a - b is multiple of 4 } . Represent this relation by a matrix. B. Using induction, prove that n2 + n is divisible by 2, where n ∊ N
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