College Algebra and Trigonometry (4th Edition)

4th Edition

ISBN: 9780134696478

Author: J. S. Ratti, Marcus S. McWaters, Leslaw Skrzypek

Publisher: PEARSON

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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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Textbook Question

Chapter 9.4, Problem 44E

In Exercises 39—48, use Cramer's Rule (if applicable) to solve each system of equations.

39. x + y = 8 x − y = − 2 40. 4 x + 3 y = − 1 2 x − 5 y = 9 41. 5 x + 3 y = 11 2 x = y = 4 42. 2 x − 7 y = 13 5 x = 6 y = 9 43. 2 x + 9 y = 4 3 x − 2 y = 6 44. 5 x + 3 y = 1 2 x − 5 y = − 12 45. 2 x − 3 y = 4 4 x − 6 y = 8 46. 3 x + y = 2 6 x + 2 y = 4 47. 2 x + 3 y = 2 5 x + 8 y = 31 6 48. 3 x − 6 y = 2 4 x + 7 y = − 3

[Hint: For Exercises 47 and 48, let u = 1 x and v = 1 y ]

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Chapter 9.4, Problem 43E

Chapter 9.4, Problem 45E

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Chapter 9 Solutions

College Algebra and Trigonometry (4th Edition)

Ch. 9.1 - A matrix is any rectangular array of...Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Prob. 8E Ch. 9.1 - In Exercises 9-14, determine the order of each...Ch. 9.1 - In Exercises 9-14, determine the order of each...

Ch. 9.1 - Prob. 11E Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Prob. 16E Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - In Exercises 19-24, write the augmented matrix for...Ch. 9.1 - Prob. 20E Ch. 9.1 - Prob. 21E Ch. 9.1 - Prob. 22E Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E Ch. 9.1 - Prob. 30E Ch. 9.1 - Prob. 31E Ch. 9.1 - Prob. 32E Ch. 9.1 - Prob. 33E Ch. 9.1 - Prob. 34E Ch. 9.1 - Prob. 35E Ch. 9.1 - Prob. 36E Ch. 9.1 - Prob. 37E Ch. 9.1 - Prob. 38E Ch. 9.1 - Prob. 39E Ch. 9.1 - Prob. 40E Ch. 9.1 - Prob. 41E Ch. 9.1 - Prob. 42E Ch. 9.1 - Prob. 43E Ch. 9.1 - Prob. 44E Ch. 9.1 - Prob. 45E Ch. 9.1 - Prob. 46E Ch. 9.1 - Prob. 47E Ch. 9.1 - Prob. 48E Ch. 9.1 - Prob. 49E Ch. 9.1 - Prob. 50E Ch. 9.1 - Prob. 51E Ch. 9.1 - Prob. 52E Ch. 9.1 - Prob. 53E Ch. 9.1 - Prob. 54E Ch. 9.1 - Prob. 55E Ch. 9.1 - Prob. 56E Ch. 9.1 - Prob. 57E Ch. 9.1 - Prob. 58E Ch. 9.1 - Prob. 59E Ch. 9.1 - Prob. 60E Ch. 9.1 - Prob. 61E Ch. 9.1 - Prob. 62E Ch. 9.1 - Prob. 63E Ch. 9.1 - Prob. 64E Ch. 9.1 - Prob. 65E Ch. 9.1 - Prob. 66E Ch. 9.1 - Prob. 67E Ch. 9.1 - Prob. 68E Ch. 9.1 - Prob. 69E Ch. 9.1 - Prob. 70E Ch. 9.1 - Prob. 71E Ch. 9.1 - In Exercises 69-74, solve each system of equations...Ch. 9.1 - Prob. 73E Ch. 9.1 - Prob. 74E Ch. 9.1 - Prob. 75E Ch. 9.1 - Prob. 76E Ch. 9.1 - Prob. 77E Ch. 9.1 - In Exercises 77 and 78, determine whether the...Ch. 9.1 - Prob. 79E Ch. 9.1 - Prob. 80E Ch. 9.1 - Prob. 81E Ch. 9.1 - Prob. 82E Ch. 9.1 - Heat transfer. In a study of heat transfer in a...Ch. 9.1 - Prob. 84E Ch. 9.1 - Prob. 85E Ch. 9.1 - Traffic flow. Repeat Exercise 85 for the following...Ch. 9.1 - Prob. 87E Ch. 9.1 - Prob. 88E Ch. 9.1 - Prob. 89E Ch. 9.1 - Prob. 90E Ch. 9.1 - Prob. 91E Ch. 9.1 - Prob. 92E Ch. 9.1 - Prob. 93E Ch. 9.1 - Prob. 94E Ch. 9.1 - Prob. 95E Ch. 9.1 - Prob. 96E Ch. 9.1 - Prob. 97E Ch. 9.1 - Prob. 98E Ch. 9.1 - Prob. 99E Ch. 9.1 - Prob. 100E Ch. 9.1 - Prob. 101E Ch. 9.1 - Prob. 102E Ch. 9.1 - Prob. 103E Ch. 9.1 - Prob. 104E Ch. 9.1 - Prob. 105E Ch. 9.1 - Prob. 106E Ch. 9.1 - Prob. 107E Ch. 9.1 - Prob. 108E Ch. 9.1 - Prob. 109E Ch. 9.1 - Prob. 110E Ch. 9.1 - Prob. 111E Ch. 9.1 - Prob. 112E Ch. 9.1 - Prob. 113E Ch. 9.1 - Prob. 114E Ch. 9.1 - Prob. 115E Ch. 9.1 - Prob. 116E Ch. 9.1 - Prob. 117E Ch. 9.1 - Prob. 118E Ch. 9.1 - Prob. 119E Ch. 9.1 - Prob. 120E Ch. 9.1 - Prob. 121E Ch. 9.1 - Prob. 122E Ch. 9.1 - Prob. 123E Ch. 9.1 - Prob. 124E Ch. 9.2 - Two mn matrices A=aij and B=bij are equal if...Ch. 9.2 - Prob. 2E Ch. 9.2 - Prob. 3E Ch. 9.2 - Prob. 4E Ch. 9.2 - Prob. 5E Ch. 9.2 - Prob. 6E Ch. 9.2 - Prob. 7E Ch. 9.2 - Prob. 8E Ch. 9.2 - Prob. 9E Ch. 9.2 - Prob. 10E Ch. 9.2 - In Exerciser 9-16, find the values of all...Ch. 9.2 - In Exerciser 9-16, find the values of all...Ch. 9.2 - Prob. 13E Ch. 9.2 - Prob. 14E Ch. 9.2 - In Exerciser 9-16, find the values of all...Ch. 9.2 - Prob. 16E Ch. 9.2 - In exercise 17-24, find each of the following if...Ch. 9.2 - Prob. 18E Ch. 9.2 - Prob. 19E Ch. 9.2 - Prob. 20E Ch. 9.2 - Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - In Exercise 25-32, solve each matrix equation for...Ch. 9.2 - In Exercise 25-32, solve each matrix equation for...Ch. 9.2 - In Exercise 25-32, solve each matrix equation for...Ch. 9.2 - In Exercise 25-32, solve each matrix equation for...Ch. 9.2 - In Exercise 25-32, solve each matrix equation for...Ch. 9.2 - Prob. 30E Ch. 9.2 - Prob. 31E Ch. 9.2 - In Exercise 25-32, solve each matrix equation for...Ch. 9.2 - In Exercise 33-42, find each product if possible....Ch. 9.2 - In Exercise 33-42, find each product if possible....Ch. 9.2 - In Exercise 33-42, find each product if possible....Ch. 9.2 - In Exercise 33-42, find each product if possible....Ch. 9.2 - In Exercise 33-42, find each product if possible....Ch. 9.2 - In Exercise 33-42, find each product if possible....Ch. 9.2 - In Exercise 33-42, find each product if possible....Ch. 9.2 - In Exercise 33-42, find each product if possible....Ch. 9.2 - In Exercise 33-42, find each product if possible....Ch. 9.2 - In Exercise 33-42, find each product if possible....Ch. 9.2 - Prob. 43E Ch. 9.2 - Prob. 44E Ch. 9.2 - Prob. 45E Ch. 9.2 - Prob. 46E Ch. 9.2 - Prob. 47E Ch. 9.2 - Prob. 48E Ch. 9.2 - Prob. 49E Ch. 9.2 - 50 Cost matrix. Repeat Exercise 49 if the order...Ch. 9.2 - Prob. 51E Ch. 9.2 - Prob. 52E Ch. 9.2 - Prob. 53E Ch. 9.2 - Prob. 54E Ch. 9.2 - Prob. 55E Ch. 9.2 - Prob. 56E Ch. 9.2 - Prob. 57E Ch. 9.2 - Prob. 58E Ch. 9.2 - Prob. 59E Ch. 9.2 - Prob. 60E Ch. 9.2 - Prob. 61E Ch. 9.2 - Prob. 62E Ch. 9.2 - Prob. 63E Ch. 9.2 - Prob. 64E Ch. 9.2 - Prob. 65E Ch. 9.2 - Prob. 66E Ch. 9.2 - Prob. 67E Ch. 9.2 - Let A=235145134 and B=135135135 Verify that AB =...Ch. 9.2 - Select appropriate 2 ( 2 matrices A and B to show...Ch. 9.2 - Prob. 70E Ch. 9.2 - Prob. 71E Ch. 9.2 - Prob. 72E Ch. 9.2 - Prob. 73E Ch. 9.2 - Prob. 74E Ch. 9.2 - Find x and y if 4213102121234211=xy Ch. 9.2 - Prob. 76E Ch. 9.2 - Prob. 77E Ch. 9.2 - Prob. 78E Ch. 9.2 - Prob. 79E Ch. 9.2 - Prob. 80E Ch. 9.2 - Prob. 81E Ch. 9.2 - Prob. 82E Ch. 9.2 - Prob. 83E Ch. 9.2 - Prob. 84E Ch. 9.2 - Prob. 85E Ch. 9.2 - Prob. 86E Ch. 9.2 - Prob. 87E Ch. 9.2 - Prob. 88E Ch. 9.2 - Prob. 89E Ch. 9.2 - Prob. 90E Ch. 9.2 - Prob. 91E Ch. 9.2 - Prob. 92E Ch. 9.2 - Prob. 93E Ch. 9.2 - Prob. 94E Ch. 9.2 - Prob. 95E Ch. 9.2 - Prob. 96E Ch. 9.2 - Prob. 97E Ch. 9.2 - In exercise 95-98, solve each system....Ch. 9.3 - For n × n matrices A and B, if AB = I = BA, then B...Ch. 9.3 - Prob. 2E Ch. 9.3 - To find the inverse of an invertible matrix A, we...Ch. 9.3 - Prob. 4E Ch. 9.3 - Prob. 5E Ch. 9.3 - Prob. 6E Ch. 9.3 - Prob. 7E Ch. 9.3 - Prob. 8E Ch. 9.3 - In Exercises 9-18, determine whether B is the...Ch. 9.3 - Prob. 10E Ch. 9.3 - Prob. 11E Ch. 9.3 - Prob. 12E Ch. 9.3 - Prob. 13E Ch. 9.3 - Prob. 14E Ch. 9.3 - Prob. 15E Ch. 9.3 - Prob. 16E Ch. 9.3 - Prob. 17E Ch. 9.3 - Prob. 18E Ch. 9.3 - Prob. 19E Ch. 9.3 - Prob. 20E Ch. 9.3 - Prob. 21E Ch. 9.3 - Prob. 22E Ch. 9.3 - Prob. 23E Ch. 9.3 - Prob. 24E Ch. 9.3 - Prob. 25E Ch. 9.3 - Prob. 26E Ch. 9.3 - Prob. 27E Ch. 9.3 - Prob. 28E Ch. 9.3 - Prob. 29E Ch. 9.3 - Prob. 30E Ch. 9.3 - Prob. 31E Ch. 9.3 - Prob. 32E Ch. 9.3 - Prob. 33E Ch. 9.3 - Prob. 34E Ch. 9.3 - Prob. 35E Ch. 9.3 - Prob. 36E Ch. 9.3 - Prob. 37E Ch. 9.3 - Prob. 38E Ch. 9.3 - Prob. 39E Ch. 9.3 - Prob. 40E Ch. 9.3 - In Exercises 39—42, write each matrix equation as...Ch. 9.3 - Prob. 42E Ch. 9.3 - Prob. 43E Ch. 9.3 - Prob. 44E Ch. 9.3 - Prob. 45E Ch. 9.3 - Prob. 46E Ch. 9.3 - a. Find the inverse of the matrix A=111123149 . b....Ch. 9.3 - Prob. 48E Ch. 9.3 - Prob. 49E Ch. 9.3 - Prob. 50E Ch. 9.3 - Prob. 51E Ch. 9.3 - Prob. 52E Ch. 9.3 - Prob. 53E Ch. 9.3 - Prob. 54E Ch. 9.3 - Prob. 55E Ch. 9.3 - Prob. 56E Ch. 9.3 - Prob. 57E Ch. 9.3 - Prob. 58E Ch. 9.3 - Prob. 59E Ch. 9.3 - Prob. 60E Ch. 9.3 - Prob. 61E Ch. 9.3 - Prob. 62E Ch. 9.3 - Prob. 63E Ch. 9.3 - Prob. 64E Ch. 9.3 - Prob. 65E Ch. 9.3 - Prob. 66E Ch. 9.3 - Prob. 67E Ch. 9.3 - Prob. 68E Ch. 9.3 - Prob. 69E Ch. 9.3 - Prob. 70E Ch. 9.3 - Prob. 71E Ch. 9.3 - Prob. 72E Ch. 9.3 - Prob. 73E Ch. 9.3 - Prob. 74E Ch. 9.3 - Prob. 75E Ch. 9.3 - Prob. 76E Ch. 9.3 - Prob. 77E Ch. 9.3 - Prob. 78E Ch. 9.3 - Prob. 79E Ch. 9.3 - Prob. 80E Ch. 9.3 - Prob. 81E Ch. 9.3 - Prob. 82E Ch. 9.3 - Prob. 83E Ch. 9.3 - Prob. 84E Ch. 9.3 - Prob. 85E Ch. 9.3 - Prob. 86E Ch. 9.3 - Prob. 87E Ch. 9.3 - Prob. 88E Ch. 9.3 - Prob. 89E Ch. 9.3 - Prob. 90E Ch. 9.3 - Prob. 91E Ch. 9.3 - Prob. 92E Ch. 9.3 - Prob. 93E Ch. 9.3 - Prob. 94E Ch. 9.3 - Prob. 95E Ch. 9.3 - Prob. 96E Ch. 9.3 - Prob. 97E Ch. 9.4 - The determinant of abcd is______________.Ch. 9.4 - The minor of an element is the determinant you get...Ch. 9.4 - To expand an n × n determinant, you multiply each...Ch. 9.4 - A system of n linear equations in n variables has...Ch. 9.4 - True or False. A 2 by 2 determinant is always...Ch. 9.4 - Prob. 6E Ch. 9.4 - Prob. 7E Ch. 9.4 - Prob. 8E Ch. 9.4 - In Exercises 9—18, evaluate each determinant. 9. 2...Ch. 9.4 - Prob. 10E Ch. 9.4 - Prob. 11E Ch. 9.4 - In Exercises 9—18, evaluate each determinant. 9. 2...Ch. 9.4 - Prob. 13E Ch. 9.4 - Prob. 14E Ch. 9.4 - Prob. 15E Ch. 9.4 - Prob. 16E Ch. 9.4 - In Exercises 9—18, evaluate each determinant. 9. 2...Ch. 9.4 - Prob. 18E Ch. 9.4 - For Exercises 19—22, consider the matrix...Ch. 9.4 - For Exercises 19—22, consider the matrix...Ch. 9.4 - Prob. 21E Ch. 9.4 - Prob. 22E Ch. 9.4 - Prob. 23E Ch. 9.4 - Prob. 24E Ch. 9.4 - Prob. 25E Ch. 9.4 - Prob. 26E Ch. 9.4 - Prob. 27E Ch. 9.4 - Prob. 28E Ch. 9.4 - Prob. 29E Ch. 9.4 - Prob. 30E Ch. 9.4 - In Exercises 23—38, evaluate each determinant. 23....Ch. 9.4 - Prob. 32E Ch. 9.4 - Prob. 33E Ch. 9.4 - Prob. 34E Ch. 9.4 - Prob. 35E Ch. 9.4 - Prob. 36E Ch. 9.4 - Prob. 37E Ch. 9.4 - In Exercises 23—38, evaluate each determinant. 23....Ch. 9.4 - Prob. 39E Ch. 9.4 - Prob. 40E Ch. 9.4 - Prob. 41E Ch. 9.4 - Prob. 42E Ch. 9.4 - Prob. 43E Ch. 9.4 - In Exercises 39—48, use Cramer's Rule (if...Ch. 9.4 - Prob. 45E Ch. 9.4 - In Exercises 39—48, use Cramer's Rule (if...Ch. 9.4 - Prob. 47E Ch. 9.4 - Prob. 48E Ch. 9.4 - Prob. 49E Ch. 9.4 - Prob. 50E Ch. 9.4 - Prob. 51E Ch. 9.4 - Prob. 52E Ch. 9.4 - Prob. 53E Ch. 9.4 - Prob. 54E Ch. 9.4 - Prob. 55E Ch. 9.4 - Prob. 56E Ch. 9.4 - Prob. 57E Ch. 9.4 - Prob. 58E Ch. 9.4 - Prob. 59E Ch. 9.4 - Prob. 60E Ch. 9.4 - Prob. 61E Ch. 9.4 - Prob. 62E Ch. 9.4 - Prob. 63E Ch. 9.4 - Prob. 64E Ch. 9.4 - Prob. 65E Ch. 9.4 - Prob. 66E Ch. 9.4 - Prob. 67E Ch. 9.4 - Prob. 68E Ch. 9.4 - Prob. 69E Ch. 9.4 - Prob. 70E Ch. 9.4 - Prob. 71E Ch. 9.4 - Prob. 72E Ch. 9.4 - Prob. 73E Ch. 9.4 - Prob. 74E Ch. 9.4 - Prob. 75E Ch. 9.4 - Prob. 76E Ch. 9.4 - Prob. 77E Ch. 9.4 - Prob. 78E Ch. 9.4 - Prob. 79E Ch. 9.4 - Prob. 80E Ch. 9.4 - Prob. 81E Ch. 9.4 - Prob. 82E Ch. 9.4 - Prob. 83E Ch. 9.4 - Prob. 84E Ch. 9.4 - Prob. 85E Ch. 9.4 - Prob. 86E Ch. 9.4 - Prob. 87E Ch. 9.4 - Prob. 88E Ch. 9.4 - Prob. 89E Ch. 9.4 - Prob. 90E Ch. 9.4 - Prob. 91E Ch. 9.4 - Prob. 92E Ch. 9.4 - Prob. 93E Ch. 9.4 - Prob. 94E Ch. 9.4 - Prob. 95E Ch. 9.4 - Prob. 96E Ch. 9.4 - Prob. 97E Ch. 9.4 - Prob. 98E Ch. 9.4 - Prob. 99E Ch. 9.4 - Find the values of a and b for which the system of...Ch. 9.4 - Prob. 101E Ch. 9.4 - Prob. 102E Ch. 9.4 - Prob. 103E Ch. 9.4 - Prob. 104E Ch. 9.4 - Prob. 105E Ch. 9.4 - Prob. 106E Ch. 9.4 - Prob. 107E Ch. 9.4 - Prob. 108E Ch. 9.4 - Prob. 109E Ch. 9.4 - Prob. 110E Ch. 9 - Prob. 1RE Ch. 9 - Prob. 2RE Ch. 9 - Prob. 3RE Ch. 9 - Prob. 4RE Ch. 9 - Prob. 5RE Ch. 9 - Prob. 6RE Ch. 9 - In Exercises 7 and 8, write the augmented matrix...Ch. 9 - In Exercises 7 and 8, write the augmented matrix...Ch. 9 - Prob. 9RE Ch. 9 - In Exercise 9 and 10 each matrix to row-echelon...Ch. 9 - Prob. 11RE Ch. 9 - Prob. 12RE Ch. 9 - Prob. 13RE Ch. 9 - In Exercise 13-16, solve each system of equation...Ch. 9 - Prob. 15RE Ch. 9 - Prob. 16RE Ch. 9 - Prob. 17RE Ch. 9 - Prob. 18RE Ch. 9 - Prob. 19RE Ch. 9 - Prob. 20RE Ch. 9 - Prob. 21RE Ch. 9 - Prob. 22RE Ch. 9 - Prob. 23RE Ch. 9 - Prob. 24RE Ch. 9 - Prob. 25RE Ch. 9 - Prob. 26RE Ch. 9 - Prob. 27RE Ch. 9 - Prob. 28RE Ch. 9 - Prob. 29RE Ch. 9 - Prob. 30RE Ch. 9 - Prob. 31RE Ch. 9 - Prob. 32RE Ch. 9 - Prob. 33RE Ch. 9 - Prob. 34RE Ch. 9 - Prob. 35RE Ch. 9 - Prob. 36RE Ch. 9 - Prob. 37RE Ch. 9 - Prob. 38RE Ch. 9 - Prob. 39RE Ch. 9 - Prob. 40RE Ch. 9 - Prob. 41RE Ch. 9 - Prob. 42RE Ch. 9 - Prob. 43RE Ch. 9 - Prob. 44RE Ch. 9 - Prob. 45RE Ch. 9 - Prob. 46RE Ch. 9 - Prob. 47RE Ch. 9 - Prob. 48RE Ch. 9 - Prob. 49RE Ch. 9 - Prob. 50RE Ch. 9 - Prob. 51RE Ch. 9 - Prob. 52RE Ch. 9 - Prob. 53RE Ch. 9 - Prob. 54RE Ch. 9 - Prob. 55RE Ch. 9 - Prob. 56RE Ch. 9 - Prob. 57RE Ch. 9 - Prob. 58RE Ch. 9 - Prob. 59RE Ch. 9 - Prob. 60RE Ch. 9 - Prob. 61RE Ch. 9 - Prob. 62RE Ch. 9 - Prob. 63RE Ch. 9 - Prob. 64RE Ch. 9 - Prob. 65RE Ch. 9 - Prob. 66RE Ch. 9 - Prob. 67RE Ch. 9 - Prob. 68RE Ch. 9 - Prob. 69RE Ch. 9 - Prob. 70RE Ch. 9 - 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