Explanation Given information: A = [ 1 0 2 3 2 1 4 0 3 ] B = [ 1 1 3 0 4 2 1 1 3 2 0 1 ] C = [ 5 3 1 2 ] D = [ 4 2 3 5 ] E = [ 1 0 4 5 1 0 ] F = [ 1 0 − 1 3 2 − 1 3 − 4 ] . Formula used: Scalar Multiplication: Multiplying a matrix by a real number results in a matrix in which each entry of the original matrix is multiplied by the real number. Thus, if A = [ a 11 a 12 a 21 a 22 ] , then c A = [ c ⋅ a 11 c ⋅ a 12 c ⋅ a 21 c ⋅ a 22 ] . If Matrix A is of order m × n and matrix B is of order n × p , the product of A and B is A B with order m × p , with the i j entry of A B given by the formula A B i j = a i 1 b 1 j + a i 2 b 2 j + ....... + a i n b n j . Two matrices are said to be equal if they are of the same order and each element in one equals to the corresponding element in the other. Calculation: To find the product of ( 1 4 A ) B , first simplify 1 4 A . 1 4 A = 1 4 [ 1 0 2 3 2 1 4 0 3 ] = [ 1 ⋅ 1 4 0 ⋅ 1 4 2 ⋅ 1 4 3 ⋅ 1 4 2 ⋅ 1 4 1 ⋅ 1 4 4 ⋅ 1 4 0 ⋅ 1 4 3 ⋅ 1 4 ] = [ 1 4 0 1 2 3 4 1 2 1 4 1 0 3 4 ] . Now multiply matrix B to the matrix above. ( 1 4 A ) B = [ 1 4 0 1 2 3 4 1 2 1 4 1 0 3 4 ] [ 1 1 3 0 4 2 1 1 3 2 0 1 ] . ⇒ [ 1 4 ⋅ 1 + 0 ⋅ 4 + 1 2 ⋅ 3 1 4 ⋅ 1 + 0 ⋅ 2 + 1 2 ⋅ 2 1 4 ⋅ 3 + 0 ⋅ 1 + 1 2 ⋅ 0 1 4 ⋅ 0 + 0 ⋅ 1 + 1 2 ⋅ 1 3 4 ⋅ 1 + 1 2 ⋅ 4 + 1 4 ⋅ 3 3 4 ⋅ 1 + 1 2 ⋅ 2 + 1 4 ⋅ 2 3 4 ⋅ 3 + 1 2 ⋅ 1 + 1 4 ⋅ 0 3 4 ⋅ 0 + 1 2 ⋅ 1 + 1 4 ⋅ 1 1 ⋅ 1 + 0 ⋅ 4 + 3 4 ⋅ 3 1 ⋅ 1 + 0 ⋅ 2 + 3 4 ⋅ 2 1 ⋅ 3 + 0 ⋅ 1 + 3 4 ⋅ 0 1 ⋅ 0 + 0 ⋅ 1 + 3 4 ⋅ 1 ] ⇒ [ 1 4 + 0 + 3 2 1 4 + 0 + 1 3 4 + 0 + 0 0 + 0 + 1 2 3 4 + 2 + 3 4 3 4 + 1 + 1 2 9 4 + 1 2 + 0 0 + 1 2 + 1 4 1 + 0 + 9 4 1 + 0 + 6 4 3 + 0 + 0 0 + 0 + 3 4 ] ⇒ [ 7 4 5 4 3 4 1 2 7 2 9 4 11 4 3 4 13 4 5 2 3 3 4 ]

Mathematical Applications for the Management, Life, and Social Sciences

11th Edition

ISBN: 9781305108042

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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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 ar…

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Question

Chapter 3.2, Problem 22E

To determine

Whether (14A)B is equal to 14(AB), where A=[102321403] and B=[113042113201].

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Chapter 3.2, Problem 21E

Chapter 3.2, Problem 23E

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Chapter 3 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 3.1 - (a) Do matrices A and B have the same...Ch. 3.1 - Ch. 3.1 - 3. (a) What matrix D must be added to matrix A...Ch. 3.1 - Prob. 4CP Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Prob. 4E Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...

Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Use the following matrices for Problems...Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - In Problems 15-28, perform the operations if...Ch. 3.1 - Prob. 25E Ch. 3.1 - In Problems 15-28, perform the operations if...Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - In Problems , find and. Ch. 3.1 - In Problems , find and. Ch. 3.1 - Prob. 33E Ch. 3.1 - 34. Find and if Ch. 3.1 - Endangered species The tables below give the...Ch. 3.1 - 36. Asian demographics The following tables show...Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Sales Let MatrixA represent the sales (in...Ch. 3.1 - 40. Opinion polls A poll of people revealed...Ch. 3.1 - Prob. 41E Ch. 3.1 - Weekly earnings The following table shows median...Ch. 3.1 - Prob. 43E Ch. 3.1 - 44. Debt payment Ace, Baker, and Champ are being...Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - 47. Management Management is attempting to...Ch. 3.1 - 48. Ranking To rank the five members of a...Ch. 3.1 - 49. Production and inventories Operating from two...Ch. 3.1 - Prob. 50E Ch. 3.1 - 51. Management In an evaluation of labor...Ch. 3.1 - Prob. 52E Ch. 3.1 - 53. For the data in the Problem , use an Excel...Ch. 3.1 - 54. For the data in problem, use an Excel...Ch. 3.2 - What is element if with and Ch. 3.2 - 2. Find the product. and Ch. 3.2 - 3. (a) Compute if and (b) Can the product...Ch. 3.2 - In Problems 1 and 2, multiply the matrices. (a)[1...Ch. 3.2 - In Problems 1 and 2, multiply the matrices. (a)[2...Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - Prob. 12E Ch. 3.2 - In Problems 5-24, use matrices through. In...Ch. 3.2 - Prob. 14E Ch. 3.2 - Prob. 15E Ch. 3.2 - Prob. 16E Ch. 3.2 - Prob. 17E Ch. 3.2 - Prob. 18E Ch. 3.2 - Prob. 19E Ch. 3.2 - Prob. 20E Ch. 3.2 - Prob. 21E Ch. 3.2 - Prob. 22E Ch. 3.2 - In Problems 25-34, use the matrices below....Ch. 3.2 - Prob. 24E Ch. 3.2 - Prob. 25E Ch. 3.2 - Prob. 26E Ch. 3.2 - Prob. 27E Ch. 3.2 - Prob. 28E Ch. 3.2 - Prob. 29E Ch. 3.2 - Prob. 30E Ch. 3.2 - Prob. 31E Ch. 3.2 - Prob. 32E Ch. 3.2 - Is it true for matrices (as it is for real...Ch. 3.2 - Prob. 34E Ch. 3.2 - Prob. 35E Ch. 3.2 - 38. For Are and defined? What size is each...Ch. 3.2 - Prob. 37E Ch. 3.2 - In each of Problems , substitute the given values...Ch. 3.2 - Prob. 39E Ch. 3.2 - Prob. 40E Ch. 3.2 - Prob. 41E Ch. 3.2 - Prob. 42E Ch. 3.2 - 45. Car pricing A car dealer can buy midsize cars...Ch. 3.2 - . Revenue A clothing manufacturer has factories...Ch. 3.2 - Prob. 45E Ch. 3.2 - . Area and population Matrix below gives the...Ch. 3.2 - 49. Population dynamics Suppose that for a...Ch. 3.2 - 50. Nutrition Suppose the weights (in grams) and...Ch. 3.2 - Prob. 49E Ch. 3.2 - Encoding messages Multiplication by a matrix can...Ch. 3.2 - 54. Production A manufacturer of small kitchen...Ch. 3.2 - 55. Accounting The annual budget of the Magnum...Ch. 3.2 - Prob. 54E Ch. 3.3 - CHECKPOINT (a) Write the augmented matrix for...Ch. 3.3 - Prob. 2CP Ch. 3.3 - CHECKPOINT For each system of equations, the...Ch. 3.3 - CHECKPOINT For each system of equations, the...Ch. 3.3 - Prob. 5CP Ch. 3.3 - In a problem 1 and 2 use the indicated row...Ch. 3.3 - In problem 1 and 2, use the indicated row...Ch. 3.3 - In problem 3 and 4, write the augmented matrix...Ch. 3.3 - In problem 3 and 4, write the augmented matrix...Ch. 3.3 - In problem 5-10, an augmented matrix for a...Ch. 3.3 - Prob. 6E Ch. 3.3 - In problem 5-10, an augmented matrix for a system...Ch. 3.3 - In problem 5-10, an augmented matrix for a system...Ch. 3.3 - In problem 5-10, an augmented matrix for a system...Ch. 3.3 - Prob. 10E Ch. 3.3 - In problem 11-16, use row operations on...Ch. 3.3 - In problem 11-16, use row operations on...Ch. 3.3 - In problem 11-16, use row operations on augmented...Ch. 3.3 - In problem 11-16, use row operations on augmented...Ch. 3.3 - Prob. 15E Ch. 3.3 - Prob. 16E Ch. 3.3 - In problem 17- 20, a system of linear equations...Ch. 3.3 - In problem 17- 20, a system of linear equations...Ch. 3.3 - In problem 17- 20, a system of linear equations...Ch. 3.3 - In problem 17- 20, a system of linear equations...Ch. 3.3 - Prob. 21E Ch. 3.3 - Prob. 22E Ch. 3.3 - Prob. 23E Ch. 3.3 - In systems of equations in problem 23 – 36 may...Ch. 3.3 - Prob. 25E Ch. 3.3 - Prob. 26E Ch. 3.3 - Prob. 27E Ch. 3.3 - Prob. 29E Ch. 3.3 - In systems of equations in problem 23 – 36 may...Ch. 3.3 - Prob. 30E Ch. 3.3 - Prob. 31E Ch. 3.3 - In systems of equations in problem 23 – 36 may...Ch. 3.3 - Prob. 33E Ch. 3.3 - In systems of equations in problem 23 – 36 may...Ch. 3.3 - Prob. 35E Ch. 3.3 - Prob. 36E Ch. 3.3 - Prob. 37E Ch. 3.3 - Prob. 38E Ch. 3.3 - Prob. 39E Ch. 3.3 - Prob. 40E Ch. 3.3 - Prob. 41E Ch. 3.3 - Prob. 43E Ch. 3.3 - Prob. 44E Ch. 3.3 - Prob. 45E Ch. 3.3 - Prob. 46E Ch. 3.3 - Prob. 47E Ch. 3.3 - Prob. 48E Ch. 3.3 - 45. Nutrition A preschool has Campbell’s Chunky...Ch. 3.3 - 46. Ticket sales A 3500-seat theatre sells...Ch. 3.3 - 47. Investment A man has $235,000 invested in...Ch. 3.3 - 48. Loans A bank lent $1.2 million for the...Ch. 3.3 - 49. Car rental patterns A car rental agency in...Ch. 3.3 - 50. Nutrition A psychologist studying the...Ch. 3.3 - 51. Nutrition The following table gives the...Ch. 3.3 - 52. Investment A brokerage house offers three...Ch. 3.3 - Investment Suppose that portfolios I and II in...Ch. 3.3 - 54. Nutrition Each ounce of substance A supplies...Ch. 3.3 - 55. Nutrition A glass of skim milk supplies 0.1 mg...Ch. 3.3 - 56. Transportation The King Trucking Company has...Ch. 3.3 - Nutrition A botanist can purchase plant food of...Ch. 3.3 - Traffic flow In the analyst of traffic flow, a...Ch. 3.3 - Nutrition Three different bacteria are cultured in...Ch. 3.3 - Irrigation An irrigation system allows water to...Ch. 3.3 - Investment An investment club has set a goal to...Ch. 3.3 - A trust account client has to be invested. The...Ch. 3.3 - 63. Investment A brokerage house offers three...Ch. 3.4 - [Type here] CHECKPOINT Are the matricesand...Ch. 3.4 - Prob. 2CP Ch. 3.4 - Prob. 3CP Ch. 3.4 - [Type text] If is a matrix and is its inverse,...Ch. 3.4 - Prob. 2E Ch. 3.4 - Prob. 3E Ch. 3.4 - Prob. 4E Ch. 3.4 - [Type text] In Problems 5-10, find the inverse...Ch. 3.4 - [Type text] In Problems 5-10, find the inverse...Ch. 3.4 - Prob. 7E Ch. 3.4 - Prob. 8E Ch. 3.4 - Prob. 9E Ch. 3.4 - Prob. 10E Ch. 3.4 - Prob. 11E Ch. 3.4 - Prob. 12E Ch. 3.4 - Prob. 13E Ch. 3.4 - Prob. 14E Ch. 3.4 - [Type here] In Problems 15-20, find the inverse...Ch. 3.4 - Prob. 16E Ch. 3.4 - Prob. 17E Ch. 3.4 - [Type here] In Problems 15-20, find the inverse...Ch. 3.4 - Prob. 19E Ch. 3.4 - Prob. 20E Ch. 3.4 - Prob. 21E Ch. 3.4 - Prob. 22E Ch. 3.4 - [Type here] In Problems 23-26, the inverse of...Ch. 3.4 - [Type here] In Problems 23-26, the inverse of...Ch. 3.4 - [Type here] In Problems 23-26, the inverse of...Ch. 3.4 - [Type here] In Problems 23-26, the inverse of...Ch. 3.4 - Prob. 27E Ch. 3.4 - [Type here] 28. Use the inverse found in Problem...Ch. 3.4 - Prob. 29E Ch. 3.4 - Prob. 30E Ch. 3.4 - [Type here] In Problems 29-32, use inverse...Ch. 3.4 - [Type here] In Problems 29-32, use inverse...Ch. 3.4 - Prob. 33E Ch. 3.4 - Prob. 34E Ch. 3.4 - Prob. 35E Ch. 3.4 - Prob. 36E Ch. 3.4 - Prob. 37E Ch. 3.4 - Prob. 38E Ch. 3.4 - Prob. 39E Ch. 3.4 - Prob. 40E Ch. 3.4 - Prob. 41E Ch. 3.4 - Prob. 42E Ch. 3.4 - Prob. 43E Ch. 3.4 - Prob. 44E Ch. 3.4 - Prob. 45E Ch. 3.4 - Prob. 46E Ch. 3.4 - Prob. 47E Ch. 3.4 - Prob. 48E Ch. 3.4 - Prob. 49E Ch. 3.4 - Prob. 50E Ch. 3.4 - 51. Competition A product is made by only two...Ch. 3.4 - 52. Demographics Suppose that a government study...Ch. 3.4 - In Problems 53-63, set up each system of...Ch. 3.4 - In Problems 53-63, set up each system of...Ch. 3.4 - In Problems, set up each system of equations and...Ch. 3.4 - In problems , set up each system of equations...Ch. 3.4 - In Problems 5363, set up each system of equations...Ch. 3.4 - In Problems 5363, set up each system of equations...Ch. 3.4 - In Problems set up each system of equations and...Ch. 3.4 - In Problems set up each system of equations and...Ch. 3.4 - In Problems 53-63, set up each system of equations...Ch. 3.4 - In Problems set up each system of equations and...Ch. 3.5 - CHECKPOINT The following technology matrix for a...Ch. 3.5 - Prob. 2CP Ch. 3.5 - CHECKPOINT 3. Suppose a primitive economy has wood...Ch. 3.5 - Prob. 4CP Ch. 3.5 - The following technology matrix for a simple...Ch. 3.5 - For the economy in Problem 1, what industry is...Ch. 3.5 - Prob. 3E Ch. 3.5 - Prob. 4E Ch. 3.5 - The following technology matrix describes the...Ch. 3.5 - The following technology matrix describes the...Ch. 3.5 - Prob. 7E Ch. 3.5 - Prob. 8E Ch. 3.5 - Prob. 9E Ch. 3.5 - Prob. 10E Ch. 3.5 - Suppose a primitive economy consists of two...Ch. 3.5 - Suppose an economy has two industries, agriculture...Ch. 3.5 - Prob. 13E Ch. 3.5 - Prob. 14E Ch. 3.5 - Suppose the economy of an underdeveloped country...Ch. 3.5 - Suppose a simple economy with only an agricultural...Ch. 3.5 - Prob. 17E Ch. 3.5 - An underdeveloped country has an agricultural...Ch. 3.5 - A simple economy has an electronic components...Ch. 3.5 - Prob. 20E Ch. 3.5 - A primitive economy consists of a fishing industry...Ch. 3.5 - An economy has a manufacturing industry and a...Ch. 3.5 - Prob. 23E Ch. 3.5 - Prob. 24E Ch. 3.5 - Prob. 25E Ch. 3.5 - Interdepartmental costs Within a company is a...Ch. 3.5 - Suppose that an economy has three industries...Ch. 3.5 - Prob. 28E Ch. 3.5 - Suppose that the economy of a small nation has an...Ch. 3.5 - Suppose an economy has the same technology matrix...Ch. 3.5 - Suppose that a simple economy has three...Ch. 3.5 - Prob. 32E Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models....Ch. 3.5 - Problems 33-38 refer to closed Leontief models. A...Ch. 3.5 - Prob. 39E Ch. 3.5 - Card tables are made by joining legs and a top...Ch. 3.5 - Prob. 41E Ch. 3.5 - A log carrier has a body made from a -ft length of...Ch. 3 - Use the matrices below a needed to complete...Ch. 3 - Use the matrices below a needed to complete...Ch. 3 - Prob. 3RE Ch. 3 - Prob. 4RE Ch. 3 - Prob. 5RE Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Prob. 8RE Ch. 3 - Prob. 9RE Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Prob. 12RE Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Prob. 17RE Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 23RE Ch. 3 - Prob. 24RE Ch. 3 - Prob. 25RE Ch. 3 - Prob. 26RE Ch. 3 - Prob. 27RE Ch. 3 - Prob. 28RE Ch. 3 - Prob. 29RE Ch. 3 - Prob. 30RE Ch. 3 - In Problems 30-36, solve each system using...Ch. 3 - Prob. 32RE Ch. 3 - In Problems 30-36, solve each system using...Ch. 3 - Prob. 34RE Ch. 3 - Prob. 35RE Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Prob. 39RE Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - Prob. 46RE Ch. 3 - Prob. 47RE Ch. 3 - Prob. 48RE Ch. 3 - The Burr Cabinet Company manufactures bookcases...Ch. 3 - Prob. 50RE Ch. 3 - A small church choir is made up of men and women...Ch. 3 - Manufacturing Two departments of a firm, and ,...Ch. 3 - Prob. 53RE Ch. 3 - Investment A woman has to invest. She has decided...Ch. 3 - Nutrition A biologist is growing three different...Ch. 3 - Transportation An airline company has three types...Ch. 3 - Economy models An economy has a shipping industry...Ch. 3 - Economy models A simple economy has a shoe...Ch. 3 - Economy models A look at the industrial sector of...Ch. 3 - Economy models Suppose a closed Leontief model for...Ch. 3 - Prob. 1T Ch. 3 - Prob. 2T Ch. 3 - Prob. 3T Ch. 3 - Prob. 4T Ch. 3 - Prob. 5T Ch. 3 - Prob. 6T Ch. 3 - Prob. 7T Ch. 3 - Prob. 8T Ch. 3 - Prob. 9T Ch. 3 - Prob. 10T Ch. 3 - Prob. 11T Ch. 3 - Prob. 12T Ch. 3 - Prob. 13T Ch. 3 - Prob. 14T Ch. 3 - Suppose that the solution of an investment problem...Ch. 3 - Prob. 16T Ch. 3 - Prob. 17T Ch. 3 - Prob. 18T Ch. 3 - Prob. 19T Ch. 3 - Prob. 20T Ch. 3 - 21. Suppose the technology matrix for a closed...Ch. 3 - Use the following information in Problem ...Ch. 3 - Use the following information in Problem ...Ch. 3 - Prob. 24T Ch. 3 - Prob. 1EAGP1 Ch. 3 - Prob. 2EAGP1 Ch. 3 - Prob. 3EAGP1 Ch. 3 - Prob. 4EAGP1 Ch. 3 - Prob. 5EAGP1 Ch. 3 - Prob. 6EAGP1 Ch. 3 - Prob. 7EAGP1 Ch. 3 - Prob. 1EAGP2 Ch. 3 - Prob. 2EAGP2 Ch. 3 - Prob. 3EAGP2 Ch. 3 - Prob. 4EAGP2

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Whether ( 1 4 A ) B is equal to 1 4 ( A B ) , where A = [ 1 0 2 3 2 1 4 0 3 ] and B = [ 1 1 3 0 4 2 1 1 3 2 0 1 ] .

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Whether (14A)B is equal to 14(AB), where A=[102321403] and B=[113042113201].

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Chapter 3 Solutions