Please explain your solution: Note: Let f :S → S. If f(s) = s for all s E S we call f an identity function on S and writef = 1s.Example: Let f : A → B be a bijection. Then f o f-1 =?, and f-l o f =?.

Given: The function f : A→B be a bijection. To determine: The composition f∘f-1 and f-1∘f .

Answered: Example: Let f : A → B be a bijection.…

Math

Advanced Math

Example: Let f : A → B be a bijection. Then f o f-l =?, and f-l o f =?.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

See similar textbooks

Related questions

Q: The Wronskian of (X,X Select one: a. X b. x C. d.

A: To find The wronskian

Q: Let G= Z* and let * be an operation in a * b. Is a * b = ab/2 is closed under the operation?

A: Disproof by an example.

Q: Example: The function F(x, y) = xỹ from the set of ordered pairs of Boolean variables to the set…

Q: 1. f¹ B-A. 2. f is bijective. Suppose f: A→ B. Prove that the following statements are equivalent.

A: A bijection, also known as a bijective function, one-to-one correspondence, or invertible function,…

Q: Let CI(A) means the closure of A.. If A = [0, 1), Bd(A) = {5}, then Cl (A)

Q: 9. Let A be a nonempty set. Prove that if f is a bijection on A and f o f = f. then f is the…

A: Let A be a nonempty set. f:A→A be a bijective function on A. Such that f◦f = f (f◦f)(x) = ? ; for…

Q: Suppose that R1 and R2 are symmetric relations on a set A. a) Is R1 U R2 also reflexive? Is R1 ∩ R2…

A: Let A be any set with symmetric relations R1 and R2 defined on it. Hence R1 and R2 be subset of…

Q: 4. Using scientific means, simplify the given Boolean expression using 3-variable map: F (X, Y, Z) =…

Q: Use a table to express the values of each of these Boolean functions. a) F(x, y, z)= Z b) F(x, y,…

Q: d. Ris a relation on Z* such that (x, y) e R if and only if there is a positive integer n such that…

Q: U(5) is not isomorphic to U(10) اختر احدى الدجابات True False

A: U(5)=1, 2, 3, 4U(10)=1, 3, 7, 9

Q: Proposition 6. Consider the function g : Z² → Z² defined by g(m, n) = (m - function g is a…

A: Consider the function , g : ℤ2 → ℤ2 defined by , g(m,n) = (m - n , n - 2m). We need to show that ,…

Q: Let x={1,2,3,4} and y={1,2,3,4,5,6,7,8,9,10} and "f" from X to Y is given by…

Q: Z,[i] is an integral domain with: 121 elements O 49 elements 6 elements 9 elements

Q: 3. Let R and S be relations on a set A then (SoR)-1 = R-1o s-1.

Q: Let Cl(A) means the closure of A If A = [0, 1), A' = = (4), then Cl (A)

A: Closure of a set is set of all limits points and the elements of the set.

Q: Prove that f-(U B: -U(B.), %3D i=1 i=1 and n N (B.). 3=D1 i=1

Q: W 1 W2 W 3* V3 G2

Q: Let f, g,h:A + A be any bijective functions. Then (f ogoh)-1 f-1 oh-1 o g=1 is equal to the above…

Q: Let f, g,h: A→ A be any bijective functions. Then (f ogoh)-

Q: Let * be the operation on the cartersian product of real numbers R *R such that (a,x) * (b,y) =…

A: Given that, let * be the operation on the cartesian product of real numbers R*R such that (a, x) *…

Q: (2) Simplify the following expressions by using Boolean algebra. (a) F=…

Q: f (UMEGM) = UME¢ f (M)where C is a nonempty collection of subsets of C.

A: Set theory

Q: Let V = {(x,y)x,y € R}. Define addition on V as follows: (x,y)+(x)=(x +2x, 1,y,+Y,+2) Is addition…

A: Given: Let V=x,y|x,y∈ℝ. Also, the addition on V is defines as x1,y1+x2,y2=x1+2x2-1,y1+y2+2.

Q: Let What is the rank of AT A? Answer: A 3 0 0 0 0 0 5 11 −4 0 3 6 5 2 0 0 3 6 2 0 0 0 8 0 0 00 0 0

Q: questions Let F be a f.g free R-module- Verily tieat Hom (F, R) R or not. (R is^commutatine is a…

A: Given: It is given that let F be a og free R-module The objective is to varify that Hom (F,R) is a…

Q: Let x,y ∈ Rn Show that: |x + y| 2 + |x - y|2 = 2|x|2 + 2|y|2

Q: Let f,g,h: A A be any bijective functions. Then (f ogoh)-1

Q: 4 3. Let a, b, c, d E R. Define explicitly a bijection from [a, b] [c, d]. onto an

A: First of all, to define a bijection from [a, b] to [c, d], the condition d-c=b-a must be satisfied.…

Q: 1]If 9:T>V and f:ST and gof IS injective, prove that both f añd 9 are injective.

A: Injective function:- for every x1=x2 implies that f(x1)= f(x2) .or vice versa.

Q: Exercise 8.6.24. Suppose f: A → B, g: B → A, go f(a) = a, for every a e A, and • f o g(b) = b, for…

Q: [0 10] The relation R on a set represented by the matrix MR = 1 0 1 is symmetric. [0 10] True False

A: Given: Statement: The relation R on a set represented by the matrix MR=010101010 is symmetric. To…

Q: Consider the following bijections on R: f (x) = - g(x) = x – 7 Then (f o g)¯'(x) =

A: Given, fx=-x,gx=x-7 Find the value of f∘g-1x.

Q: Proposition 4.13. Let F be the CDF of a non-negative real-valued r.v. X. Then, E(X) = √ F(a) dr. IR+

A: As per the question we are given the cumulative distribution function (CDF) F(x) of a non-negative…

Q: Let f : A → B and g : B → C be bijections. (a) Prove that (go f)-1 exists. (b) Prove that (g o f)-1…

Q: A A is Hermitian A is Unitary ? N? or N?

Q: 3. Construct a bijection f: [0, 1] → (0, 1) UN.

Q: Using the theorem below to construct an alternative proof to the idea that ‘being associates’ is…

Q: Prove or disprove whether the function f (r) = a +2 is a bijection from R R %3D

Q: c. If f and g are both surjective, show that so is gof. d. Suppose that gof is surjective. Are f and…

Q: Give an example of two denes not equal X subsets of (R,Te) and (z, cof). ( Explain your answer ).

Q: 1) a) Are G1 and G2 Isomorphic? Why? b) Are A and B Isomorphic? Why? A

Q: Find examples of functions f and g such that f°g is a bijection, but g is not onto and f is not…

A: A function is said to be bijective if it is one-one and onto. We need to find f and g such that…

Q: USE DISCRETE MATHEMATICS AND ITS APPLICATIONS TO SOLVE THE QUESTION Question # 1 Determine…

A: Consider the provided question, We have to determine the given function is a bijection from R to R.…

Q: I c exists in (0, 1) such that f(c) (1)- f(0) 1-0

Q: Let -1 0] A= 0 2 2 -3 0| Prove that A'A=I.

Q: Let B be a Boolean algebra. Show that (а) ал0 — 0 (b) а V (аль) — а (c) a V (¬a A b) = a V b.

Q: Use a table to express the values of each of these Boolean functions. a) F(x, y, z)= z b) F(x, y,…

A: As per the bartleby guilde lines, you have asked more than 3 subparts, so, only the first 3 subparts…

Q: a) Let * be the operation on Z defined by a*b= a + b - 3ab for all a,b e Z. Justify the following…

Q: 5. Use a table to express the values of each of these Boolean functions. а) F(x, у, г) %3D Ху b)…

A: The values of boolean expression by using table are given as follows :

Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

100%

Please explain your solution:

Note: Let f :S → S. If f(s) = s for all s E S we call f an identity function on S and write
f = 1s.
Example: Let f : A → B be a bijection. Then f o f-1 =?, and f-l o f =?.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Operations$

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

27. Let , where and are nonempty. Prove that has the property that for every subset of if and only if is one-to-one. (Compare with Exercise 15 b.). 15. b. For the mapping , show that if , then .
For the given f:ZZ, decide whether f is onto and whether it is one-to-one. Prove that your decisions are correct. a. f(x)={ x2ifxiseven0ifxisodd b. f(x)={ 0ifxiseven2xifxisodd c. f(x)={ 2x+1ifxisevenx+12ifxisodd d. f(x)={ x2ifxisevenx32ifxisodd e. f(x)={ 3xifxiseven2xifxisodd f. f(x)={ 2x1ifxiseven2xifxisodd
12. Let and . For the given , decide whether is onto and whether it is one-to-one. Prove that your decisions are correct. a. b. c. d.
Let f(x),g(x),h(x)F[x] where f(x) and g(x) are relatively prime. If h(x)f(x), prove that h(x) and g(x) are relatively prime.
18. Let and be defined as follows. In each case, compute for arbitrary . a. b. c. d. e.
Label each of the following statements as either true or false. 3. Let where A and B are nonempty. Then for every subset S of A.
Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove that f is one-to-one. Prove that f is onto if and only if a=1 or a=1.
For an element x of an ordered integral domain D, the absolute value | x | is defined by | x |={ xifx0xif0x Prove that | x |=| x | for all xD. Prove that | x |x| x | for all xD. Prove that | xy |=| x || y | for all x,yD. Prove that | x+y || x |+| y | for all x,yD. Prove that | | x || y | || xy | for all x,yD.