Explanation Given: A = [ a b c d ] , O = [ 0 0 0 0 ] . Explanation: Assume that a d − b c ≠ 0 . Find A − 1 as follows: The aim is to bring a unit matrix in first two columns of the augmented matrix [ A | I ] to get [ I | A − 1 ] . [ a b 1 0 c d 0 1 ] Apply R 1 − a c R 2 → R 2 to get [ a b 1 0 0 b − a c d 1 − a c ] Now, apply R 2 b − a c d → R 2 to get [ a b 1 0 0 1 1 b − a c d − a c ( b c − a d c ) ] [ a b 1 0 0 1 c b c − a d − a b c − a d ] Now, apply R 1 − b R 2 → R 1 to get [ a 0 1 − b c c b − a d 0 − a b c b − a d 0 1 c c b − a d − a c b − a d ] [ a 0 − a d c b − a d a b c b − a d 0 1 c c b − a d

11th Edition

ISBN: 9780321979438

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 2.5, Problem 47E

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To prove: The matrix A−1A=I.

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Chapter 2.5, Problem 46E

Chapter 2.5, Problem 48E

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Chapter 2 Solutions

Finite Mathematics (11th Edition)

Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Use the echelon method to solve each system of...Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Use the echelon method to solve each system of...Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

Ch. 2.1 - Use the echelon method to solve each system of...Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Prob. 15E Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Prob. 17E Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Use the echelon method to solve each system of two...Ch. 2.1 - Prob. 20E Ch. 2.1 - An inconsistent system...Ch. 2.1 - Prob. 22E Ch. 2.1 - Describe what a parameter is arid why it is used...Ch. 2.1 - In your own words, describe the echelon method as...Ch. 2.1 - Prob. 25E Ch. 2.1 - Solve each system of equations. Let z be the...Ch. 2.1 - Solve each system of equations. Let z be the...Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - For each of the following systems of equations in...Ch. 2.1 - For each of the following systems of equations in...Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Groceries If 20 lb of rice and 10 lb of potatoes...Ch. 2.1 - 36. Downloads Blake Allvine spent $35.97...Ch. 2.1 - Prob. 37E Ch. 2.1 - 38. Sales An apparel shop sells skirts for $45...Ch. 2.1 - Prob. 39E Ch. 2.1 - 40. Stock Lorri Morgan has $16,000 invested in...Ch. 2.1 - Banking A bank teller has a total of 70 bills in...Ch. 2.1 - Rug Cleaning Machines Kelly Karpet Kleaners sells...Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - 48. Flight Time A flight leaves New York at 8...Ch. 2.1 - 49. The 24® Game The object of the 24 Game,...Ch. 2.2 - Write the augmented matrix fur each system. Do...Ch. 2.2 - Write the augmented matrix for each system. Do...Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Write the system of equations associated with...Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Use the indicated row operations to change each...Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - Prob. 15E Ch. 2.2 - Prob. 16E Ch. 2.2 - Prob. 17E Ch. 2.2 - Prob. 18E Ch. 2.2 - Prob. 19E Ch. 2.2 - Prob. 20E Ch. 2.2 - Use the Gauss-Jordan method to solve each system...Ch. 2.2 - Use the Gauss-Jordan method to solve each system...Ch. 2.2 - Prob. 23E Ch. 2.2 - Prob. 24E Ch. 2.2 - Prob. 25E Ch. 2.2 - Use the Gauss-Jordan method to solve each system...Ch. 2.2 - Prob. 27E Ch. 2.2 - Use the Gauss-Jordan method to solve each system...Ch. 2.2 - Prob. 29E Ch. 2.2 - Prob. 30E Ch. 2.2 - Prob. 31E Ch. 2.2 - Prob. 32E Ch. 2.2 - Prob. 33E Ch. 2.2 - Prob. 34E Ch. 2.2 - Prob. 35E Ch. 2.2 - Prob. 36E Ch. 2.2 - Prob. 37E Ch. 2.2 - Prob. 38E Ch. 2.2 - Prob. 39E Ch. 2.2 - Prob. 40E Ch. 2.2 - Prob. 41E Ch. 2.2 - Prob. 42E Ch. 2.2 - 43. On National Public Radio, the "Weekend...Ch. 2.2 - Prob. 44E Ch. 2.2 - Investments Katherine Chong invests $10,000...Ch. 2.2 - 46. Office Technology Pyro-Tech, Inc. is...Ch. 2.2 - Prob. 47E Ch. 2.2 - Prob. 48E Ch. 2.2 - Loans To get the necessary funds for a planned...Ch. 2.2 - Manufacturing Nadir, Inc. produces three models of...Ch. 2.2 - 51. Deliveries An electronics company produces...Ch. 2.2 - Tents L.L. Bean makes three sizes of Ultra Dome...Ch. 2.2 - Transportation A manufacturer purchases a part for...Ch. 2.2 - APPLY IT Transportation An auto manufacturer sends...Ch. 2.2 - Prob. 55E Ch. 2.2 - 56. Packaging A company produces four...Ch. 2.2 - Prob. 57E Ch. 2.2 - Animal Breeding An animal breeder can buy four...Ch. 2.2 - Prob. 59E Ch. 2.2 - Prob. 60E Ch. 2.2 - Prob. 61E Ch. 2.2 - Prob. 62E Ch. 2.2 - Prob. 63E Ch. 2.2 - Prob. 64E Ch. 2.2 - 65. Modeling War One of the factors that...Ch. 2.2 - Prob. 66E Ch. 2.2 - 67. Baseball Ichiro Suzuki holds the American...Ch. 2.2 - Prob. 68E Ch. 2.2 - 69. Toys One hundred toys are to be given out to...Ch. 2.2 - Prob. 70E Ch. 2.2 - Prob. 71E Ch. 2.2 - Prob. 72E Ch. 2.2 - Prob. 73E Ch. 2.3 - Prob. 1E Ch. 2.3 - Prob. 2E Ch. 2.3 - Prob. 3E Ch. 2.3 - Prob. 4E Ch. 2.3 - Decide whether each statement is true or false. If...Ch. 2.3 - Prob. 6E Ch. 2.3 - Prob. 7E Ch. 2.3 - Prob. 8E Ch. 2.3 - Prob. 9E Ch. 2.3 - Prob. 10E Ch. 2.3 - Prob. 11E Ch. 2.3 - Prob. 12E Ch. 2.3 - Prob. 13E Ch. 2.3 - Prob. 14E Ch. 2.3 - Prob. 15E Ch. 2.3 - Prob. 16E Ch. 2.3 - Prob. 17E Ch. 2.3 - Prob. 18E Ch. 2.3 - Prob. 19E Ch. 2.3 - Prob. 20E Ch. 2.3 - Prob. 21E Ch. 2.3 - Prob. 22E Ch. 2.3 - Prob. 23E Ch. 2.3 - Prob. 24E Ch. 2.3 - Prob. 25E Ch. 2.3 - Prob. 26E Ch. 2.3 - Prob. 27E Ch. 2.3 - Prob. 28E Ch. 2.3 - Prob. 29E Ch. 2.3 - Prob. 30E Ch. 2.3 - Prob. 31E Ch. 2.3 - Prob. 32E Ch. 2.3 - For matrices X=[ xyzw] and 0=[ 0000], find the...Ch. 2.3 - Prob. 34E Ch. 2.3 - Prob. 35E Ch. 2.3 - Prob. 36E Ch. 2.3 - Prob. 37E Ch. 2.3 - Prob. 38E Ch. 2.3 - Prob. 39E Ch. 2.3 - Prob. 40E Ch. 2.3 - Prob. 41E Ch. 2.3 - 42. Trading Partners The table below gives, the...Ch. 2.3 - Prob. 43E Ch. 2.3 - Prob. 44E Ch. 2.3 - Testing Medication A drug company is testing 200...Ch. 2.3 - Prob. 46E Ch. 2.3 - Prob. 47E Ch. 2.3 - Prob. 48E Ch. 2.3 - Prob. 49E Ch. 2.3 - Prob. 50E Ch. 2.4 - Let A=[ -2-403] and B=[ -6240]. Find each value....Ch. 2.4 - Prob. 2E Ch. 2.4 - Prob. 3E Ch. 2.4 - Prob. 4E Ch. 2.4 - Prob. 5E Ch. 2.4 - Let and Find each value. 6. 7B– 3A Ch. 2.4 - Prob. 7E Ch. 2.4 - Prob. 8E Ch. 2.4 - Prob. 9E Ch. 2.4 - Prob. 10E Ch. 2.4 - Prob. 11E Ch. 2.4 - Prob. 12E Ch. 2.4 - To find the product matrix AB, the number of...Ch. 2.4 - Prob. 14E Ch. 2.4 - Prob. 15E Ch. 2.4 - Prob. 16E Ch. 2.4 - Prob. 17E Ch. 2.4 - Prob. 18E Ch. 2.4 - Find each matrix product, if possible. 19. Ch. 2.4 - Find each matrix product, if possible. [...Ch. 2.4 - Prob. 21E Ch. 2.4 - Prob. 22E Ch. 2.4 - Prob. 23E Ch. 2.4 - Prob. 24E Ch. 2.4 - Prob. 25E Ch. 2.4 - Prob. 26E Ch. 2.4 - Prob. 27E Ch. 2.4 - Prob. 28E Ch. 2.4 - Prob. 29E Ch. 2.4 - Prob. 30E Ch. 2.4 - Prob. 31E Ch. 2.4 - Prob. 32E Ch. 2.4 - Prob. 33E Ch. 2.4 - Prob. 34E Ch. 2.4 - Prob. 35E Ch. 2.4 - Prob. 36E Ch. 2.4 - Given matrices verify that the statements in...Ch. 2.4 - Prob. 38E Ch. 2.4 - Prob. 39E Ch. 2.4 - Prob. 40E Ch. 2.4 - Prob. 41E Ch. 2.4 - Prob. 42E Ch. 2.4 - Use a computer or graphing calculator arid the...Ch. 2.4 - Prob. 44E Ch. 2.4 - Prob. 45E Ch. 2.4 - Prob. 46E Ch. 2.4 - Prob. 47E Ch. 2.4 - Prob. 48E Ch. 2.4 - Prob. 49E Ch. 2.4 - Prob. 50E Ch. 2.4 - Prob. 51E Ch. 2.4 - Prob. 52E Ch. 2.4 - Prob. 53E Ch. 2.4 - Prob. 54E Ch. 2.4 - Prob. 55E Ch. 2.4 - 56. Northern Spotted Owl Population In an attempt...Ch. 2.4 - 57. World Population The 2010 birth and death...Ch. 2.5 - Prob. 1E Ch. 2.5 - Decide whether the given matrices are inverses...Ch. 2.5 - Prob. 3E Ch. 2.5 - Decide whether the given matrices are inverses of...Ch. 2.5 - Decide whether the given matrices are inverses of...Ch. 2.5 - Prob. 6E Ch. 2.5 - Prob. 7E Ch. 2.5 - Prob. 8E Ch. 2.5 - Prob. 9E Ch. 2.5 - Prob. 10E Ch. 2.5 - Prob. 11E Ch. 2.5 - Prob. 12E Ch. 2.5 - Prob. 13E Ch. 2.5 - Prob. 14E Ch. 2.5 - Prob. 15E Ch. 2.5 - Prob. 16E Ch. 2.5 - Prob. 17E Ch. 2.5 - Prob. 18E Ch. 2.5 - Prob. 19E Ch. 2.5 - Prob. 20E Ch. 2.5 - Prob. 21E Ch. 2.5 - Prob. 22E Ch. 2.5 - Find the inverse, if it exists, for each matrix. [...Ch. 2.5 - Prob. 24E Ch. 2.5 - Prob. 25E Ch. 2.5 - Prob. 26E Ch. 2.5 - Prob. 27E Ch. 2.5 - Solve each system of equations by using the...Ch. 2.5 - Solve each system of equations by using the...Ch. 2.5 - Prob. 30E Ch. 2.5 - Prob. 31E Ch. 2.5 - Prob. 32E Ch. 2.5 - Prob. 33E Ch. 2.5 - Solve each system of equations by using the...Ch. 2.5 - Solve each system of equations by using the...Ch. 2.5 - Prob. 36E Ch. 2.5 - Prob. 37E Ch. 2.5 - Prob. 38E Ch. 2.5 - Prob. 39E Ch. 2.5 - Prob. 40E Ch. 2.5 - Prob. 41E Ch. 2.5 - Prob. 42E Ch. 2.5 - Prob. 43E Ch. 2.5 - Prob. 44E Ch. 2.5 - Prob. 45E Ch. 2.5 - Prob. 46E Ch. 2.5 - Prob. 47E Ch. 2.5 - Prob. 48E Ch. 2.5 - Prob. 49E Ch. 2.5 - Prob. 50E Ch. 2.5 - Prob. 51E Ch. 2.5 - Prob. 52E Ch. 2.5 - Prob. 53E Ch. 2.5 - Prob. 54E Ch. 2.5 - Prob. 55E Ch. 2.5 - Prob. 56E Ch. 2.5 - Prob. 57E Ch. 2.5 - Prob. 58E Ch. 2.5 - Prob. 59E Ch. 2.5 - Prob. 60E Ch. 2.5 - Prob. 61E Ch. 2.5 - Solve each exercise by using the inverse of the...Ch. 2.5 - Prob. 63E Ch. 2.5 - Solve each exercise by using the inverse of the...Ch. 2.5 - Prob. 65E Ch. 2.5 - Solve each exercise by using the inverse of the...Ch. 2.6 - Find the production matrix for the following...Ch. 2.6 - Prob. 2E Ch. 2.6 - Prob. 3E Ch. 2.6 - Prob. 4E Ch. 2.6 - Prob. 5E Ch. 2.6 - Prob. 6E Ch. 2.6 - Prob. 7E Ch. 2.6 - Find the ratios of products A, B, and C using a...Ch. 2.6 - Prob. 9E Ch. 2.6 - Use a graphing calculator or computer to find the...Ch. 2.6 - Prob. 11E Ch. 2.6 - Input-Output Open Model In Exercises 11 and 12,...Ch. 2.6 - Prob. 13E Ch. 2.6 - Prob. 14E Ch. 2.6 - Input-Output Open Model In Exercises 13-16, refer...Ch. 2.6 - Input-Output Open Model In Exercises 13- refer to...Ch. 2.6 - Input-Output Open Model A primitive economy...Ch. 2.6 - Prob. 18E Ch. 2.6 - Prob. 19E Ch. 2.6 - Prob. 20E Ch. 2.6 - 21. Israeli Economy An analysis of the 1958...Ch. 2.6 - 22. Chinese Economy The 1981 Chinese economy can...Ch. 2.6 - Prob. 23E Ch. 2.6 - Prob. 24E Ch. 2.6 - Prob. 25E Ch. 2.6 - Prob. 26E Ch. 2.6 - 27. Input-Output Closed Model Use the...Ch. 2.6 - Input-Output Closed Model Suppose that production...Ch. 2.6 - Prob. 29E Ch. 2 - Find the second-order contact matrix PQ mentioned...Ch. 2 - Prob. 2EA Ch. 2 - Prob. 3EA Ch. 2 - Prob. 4EA Ch. 2 - Prob. 5EA Ch. 2 - Prob. 1RE Ch. 2 - Determine whether each of the following statements...Ch. 2 - Prob. 3RE Ch. 2 - Prob. 4RE Ch. 2 - Prob. 5RE Ch. 2 - Prob. 6RE Ch. 2 - Prob. 7RE Ch. 2 - Prob. 8RE Ch. 2 - Prob. 9RE Ch. 2 - Prob. 10RE Ch. 2 - Prob. 11RE Ch. 2 - Prob. 12RE Ch. 2 - Prob. 13RE Ch. 2 - Prob. 14RE Ch. 2 - Prob. 15RE Ch. 2 - Prob. 16RE Ch. 2 - Prob. 17RE Ch. 2 - Prob. 18RE Ch. 2 - Solve each system by the echelon method. 19. 2x -...Ch. 2 - Prob. 20RE Ch. 2 - Solve each system by the echelon method. 2x - 3y +...Ch. 2 - Prob. 22RE Ch. 2 - Prob. 23RE Ch. 2 - Prob. 24RE Ch. 2 - Prob. 25RE Ch. 2 - Prob. 26RE Ch. 2 - Prob. 27RE Ch. 2 - Prob. 28RE Ch. 2 - Prob. 29RE Ch. 2 - Prob. 30RE Ch. 2 - Prob. 31RE Ch. 2 - Prob. 32RE Ch. 2 - Prob. 33RE Ch. 2 - Prob. 34RE Ch. 2 - Prob. 35RE Ch. 2 - Prob. 36RE Ch. 2 - Prob. 37RE Ch. 2 - Prob. 38RE Ch. 2 - Prob. 39RE Ch. 2 - Given the matrices A=[ 4102369],B=[ 232240012],C=[...Ch. 2 - Prob. 41RE Ch. 2 - Prob. 42RE Ch. 2 - Prob. 43RE Ch. 2 - Prob. 44RE Ch. 2 - Prob. 45RE Ch. 2 - Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - Prob. 49RE Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Find the inverse of each matrix that has an...Ch. 2 - Prob. 53RE Ch. 2 - Prob. 54RE Ch. 2 - Prob. 55RE Ch. 2 - Prob. 56RE Ch. 2 - Prob. 57RE Ch. 2 - Prob. 58RE Ch. 2 - Prob. 59RE Ch. 2 - Prob. 60RE Ch. 2 - Prob. 61RE Ch. 2 - Prob. 62RE Ch. 2 - Prob. 63RE Ch. 2 - Prob. 64RE Ch. 2 - Prob. 65RE Ch. 2 - Prob. 66RE Ch. 2 - Prob. 67RE Ch. 2 - Prob. 68RE Ch. 2 - Prob. 69RE Ch. 2 - Prob. 70RE Ch. 2 - Prob. 71RE Ch. 2 - Filling Orders A printer has three orders for...Ch. 2 - 73. Input-Output An economy depends on two...Ch. 2 - 74. Nebraska The 1970 economy of the state of...Ch. 2 - Prob. 75RE Ch. 2 - Prob. 76RE Ch. 2 - Prob. 77RE Ch. 2 - Prob. 78RE Ch. 2 - Prob. 79RE Ch. 2 - Prob. 80RE Ch. 2 - Prob. 81RE Ch. 2 - Prob. 82RE Ch. 2 - Prob. 83RE Ch. 2 - 84. Baseball In the 2009 Major League Baseball...Ch. 2 - Prob. 85RE

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To prove: The matrix A − 1 A = I .

Solution Summary: The author explains that the aim is to bring a unit matrix in first two columns of the augmented matrix left[A|Iright].

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To prove: The matrix A−1A=I.

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Chapter 2 Solutions