Explanation Given: The given matrix is A = [ 1 2 3 4 ] and B = [ − 1 0 3 − 2 ] Concept used: We find the inverse of the matrix using the row transformation and operation method. Also we use the fact that AA − 1 = A − 1 A = I and ( A − 1 ) − 1 = A . We also use the concept of matrix multiplication and the fact that a matrix A is invertible if and only if det A ≠ 0 . Calculation: As given A = [ 1 2 3 4 ] and B = [ − 1 0 3 − 2 ] and det A = 4 − 6 = − 2 ≠ 0 and det B = 2 − 0 = 2 ≠ 0 , thus they are invertible matrices. A B = [ 1 2 3 4 ] [ − 1 0 3 − 2 ] = [ 1 × − 1 + 2 × 3 1 × 0 + 2 × ( − 2 ) 3 × − 1 + 4 × 3 3 × 0 + 4 × ( − 2 ) ] = [ − 1 + 6 0 − 4 − 3 + 12 0 − 8 ] = [ 5 − 4 9 − 8 ] det ( A B ) = 5 × ( − 8 ) − 9 × ( − 4 ) = − 40 + 36 = − 4 ≠ 0 Hence, A B is an invertible matrix. Now to find inverse of the matrix A = [ 1 2 3 4 ] and B = [ − 1 0 3 − 2 ] , we use the fact AA − 1 = A − 1 A = I and A I = A . A I = A ⇒ A [ 1 0 0 1 ] = [ 1 2 3 4 ] R 2 → R 2 − 3 R 1 ⇒ A [ 1 0 − 3 1 ] = [ 1 2 0 − 2 ] R 2 → − 1 2 R 2 ⇒ A [ 1 0 3 2 − 1 2 ] = [ 1 2 0 1 ] R 1 → R 1 − 2 R 2 ⇒ A [ − 2 1 3 2 − 1 2 ] = [ 1 0 0 1 ] Thus A − 1 = [ − 2 1 3 2 − 1 2 ] as AA − 1 = A − 1 A = I And B I = B ⇒ B [ 1 0 0 1 ] = [ − 1 0 3 − 2 ] R 1 → − R 1 ⇒ B [

Precalculus: A Unit Circle Approach with Integrated Review, Books a la Carte Edition, plus MyLab Math with Pearson eText and Worksheets -- Access Card Package (3rd Edition)

3rd Edition

ISBN: 9780134764597

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

Publisher: PEARSON

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Chapter 7.8, Problem 72E

To determine

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The matrix AB is an invertible matrix and (AB)−1=B−1A−1.

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Chapter 7.8, Problem 71E

Chapter 7.8, Problem 73E

Chapter 7 Solutions

Precalculus: A Unit Circle Approach with Integrated Review, Books a la Carte Edition, plus MyLab Math with Pearson eText and Worksheets -- Access Card Package (3rd Edition)

Ch. 7.1 - The ordered pair (a, b) is a(n) _________ of a...Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Estimate the solution(s) (if any) of each system...Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Determine whether each system is consistent or...Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Determine whether each system is consistent or...Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - Prob. 52E Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.1 - Prob. 57E Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - Prob. 60E Ch. 7.1 - Prob. 61E Ch. 7.1 - Prob. 62E Ch. 7.1 - Prob. 63E Ch. 7.1 - Prob. 64E Ch. 7.1 - Prob. 65E Ch. 7.1 - Use any method to solve each system of equations....Ch. 7.1 - Prob. 67E Ch. 7.1 - Prob. 68E Ch. 7.1 - Prob. 69E Ch. 7.1 - Prob. 70E Ch. 7.1 - Prob. 71E Ch. 7.1 - Prob. 72E Ch. 7.1 - Prob. 73E Ch. 7.1 - Prob. 74E Ch. 7.1 - Prob. 75E Ch. 7.1 - Prob. 76E Ch. 7.1 - Prob. 77E Ch. 7.1 - Prob. 78E Ch. 7.1 - Prob. 79E Ch. 7.1 - Prob. 80E Ch. 7.1 - Prob. 81E Ch. 7.1 - Prob. 82E Ch. 7.1 - Prob. 83E Ch. 7.1 - Prob. 84E Ch. 7.1 - Prob. 85E Ch. 7.1 - Prob. 86E Ch. 7.1 - Prob. 87E Ch. 7.1 - Prob. 88E Ch. 7.1 - Prob. 89E Ch. 7.1 - Prob. 90E Ch. 7.1 - Prob. 91E Ch. 7.1 - Prob. 92E Ch. 7.1 - Prob. 93E Ch. 7.1 - Prob. 94E Ch. 7.1 - Prob. 95E Ch. 7.1 - Prob. 96E Ch. 7.1 - Prob. 97E Ch. 7.1 - Prob. 98E Ch. 7.1 - Prob. 99E Ch. 7.1 - Prob. 100E Ch. 7.1 - Prob. 101E Ch. 7.1 - Prob. 102E Ch. 7.1 - Prob. 103E Ch. 7.1 - Prob. 104E Ch. 7.1 - Prob. 105E Ch. 7.1 - Prob. 106E Ch. 7.1 - Prob. 107E Ch. 7.1 - Prob. 108E Ch. 7.1 - Prob. 109E Ch. 7.1 - Prob. 110E Ch. 7.1 - Prob. 111E Ch. 7.1 - Prob. 112E Ch. 7.1 - Prob. 113E Ch. 7.1 - Prob. 114E Ch. 7.1 - Prob. 115E Ch. 7.1 - Prob. 116E Ch. 7.1 - Prob. 117E Ch. 7.1 - Prob. 118E Ch. 7.1 - Prob. 119E Ch. 7.1 - Prob. 120E Ch. 7.1 - Prob. 121E Ch. 7.1 - Prob. 122E Ch. 7.2 - Systems or equations that have the same solution...Ch. 7.2 - Prob. 2E Ch. 7.2 - Prob. 3E Ch. 7.2 - Prob. 4E Ch. 7.2 - Prob. 5E Ch. 7.2 - Prob. 6E Ch. 7.2 - Prob. 7E Ch. 7.2 - Prob. 8E Ch. 7.2 - Determine whether the given ordered triple is a...Ch. 7.2 - Prob. 10E Ch. 7.2 - Prob. 11E Ch. 7.2 - Prob. 12E Ch. 7.2 - Prob. 13E Ch. 7.2 - Prob. 14E Ch. 7.2 - Prob. 15E Ch. 7.2 - Prob. 16E Ch. 7.2 - Prob. 17E Ch. 7.2 - Prob. 18E Ch. 7.2 - Prob. 19E Ch. 7.2 - Prob. 20E Ch. 7.2 - Prob. 21E Ch. 7.2 - Prob. 22E Ch. 7.2 - Prob. 23E Ch. 7.2 - Prob. 24E Ch. 7.2 - Prob. 25E Ch. 7.2 - Prob. 26E Ch. 7.2 - Prob. 27E Ch. 7.2 - Find the solution set of each linear system....Ch. 7.2 - Prob. 29E Ch. 7.2 - Prob. 30E Ch. 7.2 - Prob. 31E Ch. 7.2 - Prob. 32E Ch. 7.2 - Prob. 33E Ch. 7.2 - Prob. 34E Ch. 7.2 - Prob. 35E Ch. 7.2 - Prob. 36E Ch. 7.2 - Prob. 37E Ch. 7.2 - Prob. 38E Ch. 7.2 - Prob. 39E Ch. 7.2 - Prob. 40E Ch. 7.2 - Prob. 41E Ch. 7.2 - Prob. 42E Ch. 7.2 - Prob. 43E Ch. 7.2 - Prob. 44E Ch. 7.2 - Prob. 45E Ch. 7.2 - Prob. 46E Ch. 7.2 - Prob. 47E Ch. 7.2 - Prob. 48E Ch. 7.2 - Use a system of equations to solve each problem...Ch. 7.2 - Use a system of equations to solve each problem...Ch. 7.2 - Prob. 51E Ch. 7.2 - Prob. 52E Ch. 7.2 - Prob. 53E Ch. 7.2 - Prob. 54E Ch. 7.2 - Prob. 55E Ch. 7.2 - Use Table 7.1 and Figure 7.10 to determine which...Ch. 7.2 - Prob. 57E Ch. 7.2 - Prob. 58E Ch. 7.2 - Prob. 59E Ch. 7.2 - Prob. 60E Ch. 7.2 - Prob. 61E Ch. 7.2 - Write a linear equation of the form that is...Ch. 7.2 - Find an equation of the parabola of the form that...Ch. 7.2 - Prob. 64E Ch. 7.2 - Prob. 65E Ch. 7.2 - Prob. 66E Ch. 7.2 - Prob. 67E Ch. 7.2 - Prob. 68E Ch. 7.2 - Prob. 69E Ch. 7.2 - Prob. 70E Ch. 7.2 - Prob. 71E Ch. 7.2 - Prob. 72E Ch. 7.2 - Prob. 73E Ch. 7.2 - Prob. 74E Ch. 7.2 - Prob. 75E Ch. 7.2 - Prob. 76E Ch. 7.2 - Prob. 77E Ch. 7.2 - Prob. 78E Ch. 7.2 - Prob. 79E Ch. 7.2 - Prob. 80E Ch. 7.2 - Prob. 81E Ch. 7.2 - Prob. 82E Ch. 7.2 - Prob. 83E Ch. 7.2 - Prob. 84E Ch. 7.2 - Prob. 85E Ch. 7.2 - Prob. 86E Ch. 7.2 - Prob. 87E Ch. 7.2 - Prob. 88E Ch. 7.2 - Prob. 89E Ch. 7.2 - Prob. 90E Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.3 - Prob. 3E Ch. 7.3 - Prob. 4E Ch. 7.3 - Prob. 5E Ch. 7.3 - Prob. 6E Ch. 7.3 - Prob. 7E Ch. 7.3 - Prob. 8E Ch. 7.3 - Prob. 9E Ch. 7.3 - Prob. 10E Ch. 7.3 - Prob. 11E Ch. 7.3 - Prob. 12E Ch. 7.3 - Prob. 13E Ch. 7.3 - Prob. 14E Ch. 7.3 - Prob. 15E Ch. 7.3 - Prob. 16E Ch. 7.3 - Prob. 17E Ch. 7.3 - Prob. 18E Ch. 7.3 - Prob. 19E Ch. 7.3 - Prob. 20E Ch. 7.3 - Prob. 21E Ch. 7.3 - Prob. 22E Ch. 7.3 - Prob. 23E Ch. 7.3 - Prob. 24E Ch. 7.3 - Prob. 25E Ch. 7.3 - Prob. 26E Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Prob. 29E Ch. 7.3 - Prob. 30E Ch. 7.3 - Prob. 31E Ch. 7.3 - Prob. 32E Ch. 7.3 - Prob. 33E Ch. 7.3 - Prob. 34E Ch. 7.3 - Prob. 35E Ch. 7.3 - Prob. 36E Ch. 7.3 - Prob. 37E Ch. 7.3 - Prob. 38E Ch. 7.3 - Prob. 39E Ch. 7.3 - Prob. 40E Ch. 7.3 - Prob. 41E Ch. 7.3 - Prob. 42E Ch. 7.3 - Prob. 43E Ch. 7.3 - Prob. 44E Ch. 7.3 - Prob. 45E Ch. 7.3 - Prob. 46E Ch. 7.3 - Prob. 47E Ch. 7.3 - Prob. 48E Ch. 7.3 - Prob. 49E Ch. 7.3 - Prob. 50E Ch. 7.3 - Prob. 51E Ch. 7.3 - Prob. 52E Ch. 7.3 - Prob. 53E Ch. 7.3 - Prob. 54E Ch. 7.3 - Prob. 55E Ch. 7.3 - Prob. 56E Ch. 7.3 - Prob. 57E Ch. 7.3 - Prob. 58E Ch. 7.3 - Prob. 59E Ch. 7.3 - Prob. 60E Ch. 7.3 - Prob. 61E Ch. 7.3 - Prob. 62E Ch. 7.3 - Prob. 63E Ch. 7.3 - Prob. 64E Ch. 7.3 - Prob. 65E Ch. 7.3 - Prob. 66E Ch. 7.3 - Prob. 67E Ch. 7.3 - Prob. 68E Ch. 7.3 - Prob. 69E Ch. 7.3 - Prob. 70E Ch. 7.3 - Prob. 71E Ch. 7.3 - Prob. 72E Ch. 7.3 - Prob. 73E Ch. 7.3 - Prob. 74E Ch. 7.3 - Prob. 75E Ch. 7.3 - Prob. 76E Ch. 7.3 - Prob. 77E Ch. 7.3 - Prob. 78E Ch. 7.3 - Prob. 79E Ch. 7.3 - Prob. 80E Ch. 7.3 - Advertising. The Fantastic Bread Company allocates...Ch. 7.3 - Prob. 82E Ch. 7.3 - Prob. 83E Ch. 7.3 - Prob. 84E Ch. 7.3 - Return on Investment. A student in a finance class...Ch. 7.3 - Prob. 86E Ch. 7.3 - Prob. 87E Ch. 7.3 - Prob. 88E Ch. 7.3 - Prob. 89E Ch. 7.3 - Prob. 90E Ch. 7.3 - Prob. 91E Ch. 7.3 - Prob. 92E Ch. 7.3 - Prob. 93E Ch. 7.3 - Prob. 94E Ch. 7.3 - Prob. 95E Ch. 7.3 - Prob. 96E Ch. 7.3 - Prob. 97E Ch. 7.3 - Prob. 98E Ch. 7.3 - Prob. 99E Ch. 7.3 - Prob. 100E Ch. 7.3 - Prob. 101E Ch. 7.3 - Prob. 102E Ch. 7.3 - Prob. 103E Ch. 7.3 - Prob. 104E Ch. 7.3 - Prob. 105E Ch. 7.3 - Prob. 106E Ch. 7.3 - Prob. 107E Ch. 7.3 - Prob. 108E Ch. 7.3 - Prob. 109E Ch. 7.3 - Prob. 110E Ch. 7.3 - Prob. 111E Ch. 7.3 - Prob. 112E Ch. 7.3 - Prob. 113E Ch. 7.3 - Prob. 114E Ch. 7.3 - Prob. 115E Ch. 7.3 - Prob. 116E Ch. 7.3 - Prob. 117E Ch. 7.3 - Prob. 118E Ch. 7.3 - Prob. 119E Ch. 7.3 - Prob. 120E Ch. 7.4 - Prob. 1E Ch. 7.4 - Prob. 2E Ch. 7.4 - Prob. 3E Ch. 7.4 - Prob. 4E Ch. 7.4 - Prob. 5E Ch. 7.4 - Prob. 6E Ch. 7.4 - Prob. 7E Ch. 7.4 - Prob. 8E Ch. 7.4 - Prob. 9E Ch. 7.4 - Prob. 10E Ch. 7.4 - Prob. 11E Ch. 7.4 - Prob. 12E Ch. 7.4 - Prob. 13E Ch. 7.4 - Prob. 14E Ch. 7.4 - Prob. 15E Ch. 7.4 - Prob. 16E Ch. 7.4 - Prob. 17E Ch. 7.4 - Prob. 18E Ch. 7.4 - Prob. 19E Ch. 7.4 - Prob. 20E Ch. 7.4 - Prob. 21E Ch. 7.4 - Prob. 22E Ch. 7.4 - Prob. 23E Ch. 7.4 - Prob. 24E Ch. 7.4 - Prob. 25E Ch. 7.4 - Prob. 26E Ch. 7.4 - Prob. 27E Ch. 7.4 - Write the system of linear equations represented...Ch. 7.4 - Perform the indicated elementary row operations in...Ch. 7.4 - Prob. 30E Ch. 7.4 - Prob. 31E Ch. 7.4 - Prob. 32E Ch. 7.4 - Prob. 33E Ch. 7.4 - Prob. 34E Ch. 7.4 - Prob. 35E Ch. 7.4 - Prob. 36E Ch. 7.4 - Prob. 37E Ch. 7.4 - Prob. 38E Ch. 7.4 - Prob. 39E Ch. 7.4 - Prob. 40E Ch. 7.4 - Prob. 41E Ch. 7.4 - Prob. 42E Ch. 7.4 - Prob. 43E Ch. 7.4 - Prob. 44E Ch. 7.4 - Prob. 45E Ch. 7.4 - Prob. 46E Ch. 7.4 - Prob. 47E Ch. 7.4 - Prob. 48E Ch. 7.4 - Prob. 49E Ch. 7.4 - Prob. 50E Ch. 7.4 - Prob. 51E Ch. 7.4 - Prob. 52E Ch. 7.4 - Prob. 53E Ch. 7.4 - Prob. 54E Ch. 7.4 - Prob. 55E Ch. 7.4 - Prob. 56E Ch. 7.4 - Prob. 57E Ch. 7.4 - Prob. 58E Ch. 7.4 - Prob. 59E Ch. 7.4 - Prob. 60E Ch. 7.4 - Prob. 61E Ch. 7.4 - Prob. 62E Ch. 7.4 - Prob. 63E Ch. 7.4 - Prob. 64E Ch. 7.4 - Prob. 65E Ch. 7.4 - Prob. 66E Ch. 7.4 - Prob. 67E Ch. 7.4 - Prob. 68E Ch. 7.4 - Prob. 69E Ch. 7.4 - Prob. 70E Ch. 7.4 - Prob. 71E Ch. 7.4 - Prob. 72E Ch. 7.4 - Prob. 73E Ch. 7.4 - Prob. 74E Ch. 7.4 - Prob. 75E Ch. 7.4 - Prob. 76E Ch. 7.4 - Prob. 77E Ch. 7.4 - Prob. 78E Ch. 7.4 - Prob. 79E Ch. 7.4 - Prob. 80E Ch. 7.4 - Prob. 81E Ch. 7.4 - Prob. 82E Ch. 7.4 - Heat transfer. In a study of heat transfer in a...Ch. 7.4 - Prob. 84E Ch. 7.4 - Prob. 85E Ch. 7.4 - Prob. 86E Ch. 7.4 - Prob. 87E Ch. 7.4 - Prob. 88E Ch. 7.4 - Solve each system of equations by Gauss-Jordan...Ch. 7.4 - Prob. 90E Ch. 7.4 - Prob. 91E Ch. 7.4 - Prob. 92E Ch. 7.4 - Prob. 93E Ch. 7.4 - Prob. 94E Ch. 7.4 - Prob. 95E Ch. 7.4 - Prob. 96E Ch. 7.4 - Prob. 97E Ch. 7.4 - Prob. 98E Ch. 7.4 - Prob. 99E Ch. 7.4 - Prob. 100E Ch. 7.4 - Prob. 101E Ch. 7.4 - Prob. 102E Ch. 7.4 - Prob. 103E Ch. 7.4 - Prob. 104E Ch. 7.4 - Prob. 105E Ch. 7.4 - Prob. 106E Ch. 7.4 - Prob. 107E Ch. 7.4 - Prob. 108E Ch. 7.4 - Prob. 109E Ch. 7.4 - Prob. 110E Ch. 7.5 - Prob. 1E Ch. 7.5 - Prob. 2E Ch. 7.5 - Prob. 3E Ch. 7.5 - Prob. 4E Ch. 7.5 - Prob. 5E Ch. 7.5 - Prob. 6E Ch. 7.5 - Prob. 7E Ch. 7.5 - Prob. 8E Ch. 7.5 - Prob. 9E Ch. 7.5 - Prob. 10E Ch. 7.5 - Prob. 11E Ch. 7.5 - Prob. 12E Ch. 7.5 - Prob. 13E Ch. 7.5 - Prob. 14E Ch. 7.5 - Prob. 15E Ch. 7.5 - Prob. 16E Ch. 7.5 - Prob. 17E Ch. 7.5 - Prob. 18E Ch. 7.5 - Prob. 19E Ch. 7.5 - Prob. 20E Ch. 7.5 - Prob. 21E Ch. 7.5 - Prob. 22E Ch. 7.5 - Prob. 23E Ch. 7.5 - Prob. 24E Ch. 7.5 - Prob. 25E Ch. 7.5 - Prob. 26E Ch. 7.5 - Prob. 27E Ch. 7.5 - Prob. 28E Ch. 7.5 - Prob. 29E Ch. 7.5 - Prob. 30E Ch. 7.5 - Evaluate each determinant. Ch. 7.5 - Prob. 32E Ch. 7.5 - Prob. 33E Ch. 7.5 - Prob. 34E Ch. 7.5 - Prob. 35E Ch. 7.5 - Prob. 36E Ch. 7.5 - Prob. 37E Ch. 7.5 - Prob. 38E Ch. 7.5 - Prob. 39E Ch. 7.5 - Prob. 40E Ch. 7.5 - Prob. 41E Ch. 7.5 - Prob. 42E Ch. 7.5 - Prob. 43E Ch. 7.5 - Prob. 44E Ch. 7.5 - Prob. 45E Ch. 7.5 - Prob. 46E Ch. 7.5 - Prob. 47E Ch. 7.5 - Prob. 48E Ch. 7.5 - Prob. 49E Ch. 7.5 - Prob. 50E Ch. 7.5 - Prob. 51E Ch. 7.5 - Prob. 52E Ch. 7.5 - Prob. 53E Ch. 7.5 - Prob. 54E Ch. 7.5 - Prob. 55E Ch. 7.5 - Prob. 56E Ch. 7.5 - Prob. 57E Ch. 7.5 - Prob. 58E Ch. 7.5 - Prob. 59E Ch. 7.5 - Prob. 60E Ch. 7.5 - Prob. 61E Ch. 7.5 - Prob. 62E Ch. 7.5 - Prob. 63E Ch. 7.5 - Prob. 64E Ch. 7.5 - Prob. 65E Ch. 7.5 - Prob. 66E Ch. 7.5 - Prob. 67E Ch. 7.5 - Equation of a line. Three points, andall lie on...Ch. 7.5 - Prob. 69E Ch. 7.5 - Prob. 70E Ch. 7.5 - Prob. 71E Ch. 7.5 - Prob. 72E Ch. 7.5 - Prob. 73E Ch. 7.5 - Prob. 74E Ch. 7.5 - Prob. 75E Ch. 7.5 - Prob. 76E Ch. 7.5 - Prob. 77E Ch. 7.5 - Prob. 78E Ch. 7.5 - Prob. 79E Ch. 7.5 - Prob. 80E Ch. 7.5 - Prob. 81E Ch. 7.5 - Prob. 82E Ch. 7.5 - Prob. 83E Ch. 7.5 - Prob. 84E Ch. 7.5 - Prob. 85E Ch. 7.5 - Prob. 86E Ch. 7.5 - Prob. 87E Ch. 7.5 - Prob. 88E Ch. 7.5 - Prob. 89E Ch. 7.5 - Prob. 90E Ch. 7.5 - Solve the system by using Cramer’s Rule. [Hint:...Ch. 7.5 - Prob. 92E Ch. 7.5 - Prob. 93E Ch. 7.5 - Prob. 94E Ch. 7.5 - Prob. 95E Ch. 7.5 - Prob. 96E Ch. 7.5 - Prob. 97E Ch. 7.5 - Prob. 98E Ch. 7.5 - Prob. 99E Ch. 7.5 - Prob. 100E Ch. 7.5 - Prob. 101E Ch. 7.5 - Prob. 102E Ch. 7.5 - Prob. 103E Ch. 7.5 - Prob. 104E Ch. 7.5 - Prob. 105E Ch. 7.6 - Prob. 1E Ch. 7.6 - Prob. 2E Ch. 7.6 - Prob. 3E Ch. 7.6 - Prob. 4E Ch. 7.6 - Prob. 5E Ch. 7.6 - Prob. 6E Ch. 7.6 - Prob. 7E Ch. 7.6 - Prob. 8E Ch. 7.6 - Prob. 9E Ch. 7.6 - Prob. 10E Ch. 7.6 - Prob. 11E Ch. 7.6 - Prob. 12E Ch. 7.6 - Prob. 13E Ch. 7.6 - Prob. 14E Ch. 7.6 - Prob. 15E Ch. 7.6 - Prob. 16E Ch. 7.6 - Prob. 17E Ch. 7.6 - Prob. 18E Ch. 7.6 - Prob. 19E Ch. 7.6 - Prob. 20E Ch. 7.6 - Prob. 21E Ch. 7.6 - Prob. 22E Ch. 7.6 - Prob. 23E Ch. 7.6 - Prob. 24E Ch. 7.6 - Prob. 25E Ch. 7.6 - Prob. 26E Ch. 7.6 - Prob. 27E Ch. 7.6 - Prob. 28E Ch. 7.6 - Prob. 29E Ch. 7.6 - Prob. 30E Ch. 7.6 - Prob. 31E Ch. 7.6 - Prob. 32E Ch. 7.6 - Prob. 33E Ch. 7.6 - Prob. 34E Ch. 7.6 - Prob. 35E Ch. 7.6 - Prob. 36E Ch. 7.6 - Prob. 37E Ch. 7.6 - Prob. 38E Ch. 7.6 - Prob. 39E Ch. 7.6 - Prob. 40E Ch. 7.6 - Prob. 41E Ch. 7.6 - Prob. 42E Ch. 7.6 - Prob. 43E Ch. 7.6 - Prob. 44E Ch. 7.6 - Prob. 45E Ch. 7.6 - Prob. 46E Ch. 7.6 - Prob. 47E Ch. 7.6 - Prob. 48E Ch. 7.6 - Prob. 49E Ch. 7.6 - Prob. 50E Ch. 7.6 - Prob. 51E Ch. 7.6 - Prob. 52E Ch. 7.6 - Prob. 53E Ch. 7.6 - Prob. 54E Ch. 7.6 - Prob. 55E Ch. 7.6 - Prob. 56E Ch. 7.6 - Prob. 57E Ch. 7.6 - Prob. 58E Ch. 7.6 - Prob. 59E Ch. 7.6 - Find the partial-fraction decomposition of each...Ch. 7.6 - Prob. 61E Ch. 7.6 - Prob. 62E Ch. 7.6 - Prob. 63E Ch. 7.6 - Prob. 64E Ch. 7.6 - Prob. 65E Ch. 7.6 - Prob. 66E Ch. 7.6 - Prob. 67E Ch. 7.6 - Prob. 68E Ch. 7.6 - Prob. 69E Ch. 7.6 - Prob. 70E Ch. 7.6 - Prob. 71E Ch. 7.6 - Prob. 72E Ch. 7.6 - Prob. 73E Ch. 7.6 - Prob. 74E Ch. 7.6 - Prob. 75E Ch. 7.6 - Prob. 76E Ch. 7.6 - Prob. 77E Ch. 7.6 - Prob. 78E Ch. 7.6 - Prob. 79E Ch. 7.6 - Prob. 80E Ch. 7.6 - Prob. 81E Ch. 7.6 - Prob. 82E Ch. 7.6 - Prob. 83E Ch. 7.6 - Prob. 84E Ch. 7.6 - Prob. 85E Ch. 7.6 - Prob. 86E Ch. 7.6 - Prob. 87E Ch. 7.6 - Prob. 88E Ch. 7.6 - Prob. 89E Ch. 7.6 - Prob. 90E Ch. 7.6 - Prob. 91E Ch. 7.6 - Prob. 92E Ch. 7.6 - Prob. 93E Ch. 7.6 - Prob. 94E Ch. 7.6 - Prob. 95E Ch. 7.6 - Prob. 96E Ch. 7.6 - Prob. 97E Ch. 7.7 - Prob. 1E Ch. 7.7 - Prob. 2E Ch. 7.7 - Prob. 3E Ch. 7.7 - Prob. 4E Ch. 7.7 - Prob. 5E Ch. 7.7 - Prob. 6E Ch. 7.7 - Prob. 7E Ch. 7.7 - Prob. 8E Ch. 7.7 - Prob. 9E Ch. 7.7 - Prob. 10E Ch. 7.7 - Prob. 11E Ch. 7.7 - Prob. 12E Ch. 7.7 - Prob. 13E Ch. 7.7 - Prob. 14E Ch. 7.7 - Prob. 15E Ch. 7.7 - Prob. 16E Ch. 7.7 - Prob. 17E Ch. 7.7 - Prob. 18E Ch. 7.7 - Prob. 19E Ch. 7.7 - Prob. 20E Ch. 7.7 - Prob. 21E Ch. 7.7 - Prob. 22E Ch. 7.7 - Prob. 23E Ch. 7.7 - Prob. 24E Ch. 7.7 - Prob. 25E Ch. 7.7 - Prob. 26E Ch. 7.7 - Prob. 27E Ch. 7.7 - Prob. 28E Ch. 7.7 - Prob. 29E Ch. 7.7 - Prob. 30E Ch. 7.7 - Prob. 31E Ch. 7.7 - Prob. 32E Ch. 7.7 - Prob. 33E Ch. 7.7 - Prob. 34E Ch. 7.7 - Prob. 35E Ch. 7.7 - Prob. 36E Ch. 7.7 - Prob. 37E Ch. 7.7 - Prob. 38E Ch. 7.7 - Prob. 39E Ch. 7.7 - Prob. 40E Ch. 7.7 - Prob. 41E Ch. 7.7 - Prob. 42E Ch. 7.7 - Prob. 43E Ch. 7.7 - Prob. 44E Ch. 7.7 - Prob. 45E Ch. 7.7 - Prob. 46E Ch. 7.7 - Prob. 47E Ch. 7.7 - Prob. 48E Ch. 7.7 - Prob. 49E Ch. 7.7 - Prob. 50E Ch. 7.7 - Prob. 51E Ch. 7.7 - Prob. 52E Ch. 7.7 - Prob. 53E Ch. 7.7 - Prob. 54E Ch. 7.7 - Prob. 55E Ch. 7.7 - Prob. 56E Ch. 7.7 - Prob. 57E Ch. 7.7 - Prob. 58E Ch. 7.7 - Prob. 59E Ch. 7.7 - Prob. 60E Ch. 7.7 - Prob. 61E Ch. 7.7 - Prob. 62E Ch. 7.7 - Prob. 63E Ch. 7.7 - Prob. 64E Ch. 7.7 - Prob. 65E Ch. 7.7 - Prob. 66E Ch. 7.7 - Prob. 67E Ch. 7.7 - Prob. 68E Ch. 7.7 - Prob. 69E Ch. 7.7 - Prob. 70E Ch. 7.7 - Prob. 71E Ch. 7.7 - Prob. 72E Ch. 7.7 - Prob. 73E Ch. 7.7 - Prob. 74E Ch. 7.7 - Prob. 75E Ch. 7.7 - Prob. 76E Ch. 7.7 - Prob. 77E Ch. 7.7 - Prob. 78E Ch. 7.7 - Prob. 79E Ch. 7.7 - Prob. 80E Ch. 7.7 - Prob. 81E Ch. 7.7 - Prob. 82E Ch. 7.7 - Prob. 83E Ch. 7.8 - Prob. 1E Ch. 7.8 - Prob. 2E Ch. 7.8 - Prob. 3E Ch. 7.8 - Prob. 4E Ch. 7.8 - Prob. 5E Ch. 7.8 - Prob. 6E Ch. 7.8 - Prob. 7E Ch. 7.8 - Prob. 8E Ch. 7.8 - Prob. 9E Ch. 7.8 - Prob. 10E Ch. 7.8 - Prob. 11E Ch. 7.8 - Prob. 12E Ch. 7.8 - Prob. 13E Ch. 7.8 - Prob. 14E Ch. 7.8 - Prob. 15E Ch. 7.8 - Prob. 16E Ch. 7.8 - Prob. 17E Ch. 7.8 - Prob. 18E Ch. 7.8 - Prob. 19E Ch. 7.8 - Prob. 20E Ch. 7.8 - Prob. 21E Ch. 7.8 - Prob. 22E Ch. 7.8 - Prob. 23E Ch. 7.8 - Prob. 24E Ch. 7.8 - Prob. 25E Ch. 7.8 - Prob. 26E Ch. 7.8 - Prob. 27E Ch. 7.8 - Prob. 28E Ch. 7.8 - Prob. 29E Ch. 7.8 - Prob. 30E Ch. 7.8 - Prob. 31E Ch. 7.8 - Prob. 32E Ch. 7.8 - Prob. 33E Ch. 7.8 - Prob. 34E Ch. 7.8 - Prob. 35E Ch. 7.8 - Prob. 36E Ch. 7.8 - Prob. 37E Ch. 7.8 - Prob. 38E Ch. 7.8 - Prob. 39E Ch. 7.8 - Prob. 40E Ch. 7.8 - Prob. 41E Ch. 7.8 - Prob. 42E Ch. 7.8 - Prob. 43E Ch. 7.8 - Prob. 44E Ch. 7.8 - Prob. 45E Ch. 7.8 - Prob. 46E Ch. 7.8 - Prob. 47E Ch. 7.8 - Prob. 48E Ch. 7.8 - Prob. 49E Ch. 7.8 - Prob. 50E Ch. 7.8 - Prob. 51E Ch. 7.8 - Prob. 52E Ch. 7.8 - Prob. 53E Ch. 7.8 - Prob. 54E Ch. 7.8 - Prob. 55E Ch. 7.8 - Prob. 56E Ch. 7.8 - Prob. 57E Ch. 7.8 - Prob. 58E Ch. 7.8 - Prob. 59E Ch. 7.8 - Prob. 60E Ch. 7.8 - Prob. 61E Ch. 7.8 - Prob. 62E Ch. 7.8 - Prob. 63E Ch. 7.8 - Prob. 64E Ch. 7.8 - Prob. 65E Ch. 7.8 - Use ainvertible coding matrix A of your...Ch. 7.8 - Prob. 67E Ch. 7.8 - Prob. 68E Ch. 7.8 - Prob. 69E Ch. 7.8 - Prob. 70E Ch. 7.8 - Prob. 71E Ch. 7.8 - Prob. 72E Ch. 7.8 - Prob. 73E Ch. 7.8 - Prob. 74E Ch. 7.8 - Prob. 75E Ch. 7.8 - Prob. 76E Ch. 7.8 - Prob. 77E Ch. 7.8 - Prob. 78E Ch. 7.8 - Prob. 79E Ch. 7.8 - Prob. 80E Ch. 7.8 - Prob. 81E Ch. 7.8 - Prob. 82E Ch. 7.8 - Prob. 83E Ch. 7.8 - Prob. 84E Ch. 7.8 - Prob. 85E Ch. 7.8 - Prob. 86E Ch. 7.8 - Prob. 87E Ch. 7.8 - Prob. 88E Ch. 7.8 - Prob. 89E Ch. 7.8 - Prob. 90E Ch. 7.8 - Prob. 91E Ch. 7.8 - Prob. 92E Ch. 7.8 - Prob. 93E Ch. 7.8 - Prob. 94E Ch. 7.8 - Prob. 95E Ch. 7 - Prob. 1RE Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - Solve each system of equations by using the method...Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Prob. 14RE Ch. 7 - Prob. 15RE Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - Prob. 19RE Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - Prob. 27RE Ch. 7 - Prob. 28RE Ch. 7 - Prob. 29RE Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE Ch. 7 - Prob. 32RE Ch. 7 - Prob. 33RE Ch. 7 - Prob. 34RE Ch. 7 - Prob. 35RE Ch. 7 - Prob. 36RE Ch. 7 - Prob. 37RE Ch. 7 - Prob. 38RE Ch. 7 - Prob. 39RE Ch. 7 - Prob. 40RE Ch. 7 - Prob. 41RE Ch. 7 - Prob. 42RE Ch. 7 - Prob. 43RE Ch. 7 - Prob. 44RE Ch. 7 - Prob. 45RE Ch. 7 - Prob. 46RE Ch. 7 - Prob. 47RE Ch. 7 - Prob. 48RE Ch. 7 - Prob. 49RE Ch. 7 - Prob. 50RE Ch. 7 - Prob. 51RE Ch. 7 - Prob. 52RE Ch. 7 - Prob. 53RE Ch. 7 - Prob. 54RE Ch. 7 - Prob. 55RE Ch. 7 - Prob. 56RE Ch. 7 - Prob. 57RE Ch. 7 - Prob. 58RE Ch. 7 - Prob. 59RE Ch. 7 - Prob. 60RE Ch. 7 - Prob. 61RE Ch. 7 - Prob. 62RE Ch. 7 - Prob. 63RE Ch. 7 - Prob. 64RE Ch. 7 - Prob. 65RE Ch. 7 - Prob. 66RE Ch. 7 - Prob. 67RE Ch. 7 - Prob. 68RE Ch. 7 - Prob. 69RE Ch. 7 - Prob. 70RE Ch. 7 - Prob. 71RE Ch. 7 - Prob. 72RE Ch. 7 - Prob. 73RE Ch. 7 - Prob. 74RE Ch. 7 - Prob. 75RE Ch. 7 - Prob. 76RE Ch. 7 - Prob. 77RE Ch. 7 - Paper route. Chris covers her paper route, which...Ch. 7 - Agriculture. A rectangular pasture with an area...Ch. 7 - Prob. 80RE Ch. 7 - Prob. 81RE Ch. 7 - Prob. 82RE Ch. 7 - Prob. 83RE Ch. 7 - Prob. 84RE Ch. 7 - Passing a final exam. Twenty-six students in a...Ch. 7 - Prob. 86RE Ch. 7 - Prob. 87RE Ch. 7 - Prob. 88RE Ch. 7 - Prob. 89RE Ch. 7 - Prob. 90RE Ch. 7 - Prob. 91RE Ch. 7 - Prob. 92RE Ch. 7 - Building houses. A builder hasunits of material...Ch. 7 - Prob. 94RE Ch. 7 - Prob. 1PTA Ch. 7 - Prob. 2PTA Ch. 7 - Prob. 3PTA Ch. 7 - Prob. 4PTA Ch. 7 - Prob. 5PTA Ch. 7 - Prob. 6PTA Ch. 7 - Prob. 7PTA Ch. 7 - Prob. 8PTA Ch. 7 - Prob. 9PTA Ch. 7 - Prob. 10PTA Ch. 7 - Prob. 11PTA Ch. 7 - Prob. 12PTA Ch. 7 - Prob. 13PTA Ch. 7 - Prob. 14PTA Ch. 7 - Prob. 15PTA Ch. 7 - Prob. 16PTA Ch. 7 - Prob. 17PTA Ch. 7 - Prob. 18PTA Ch. 7 - Prob. 19PTA Ch. 7 - Prob. 20PTA Ch. 7 - Prob. 1PTB Ch. 7 - Prob. 2PTB Ch. 7 - Prob. 3PTB Ch. 7 - Prob. 4PTB Ch. 7 - Prob. 5PTB Ch. 7 - Prob. 6PTB Ch. 7 - Prob. 7PTB Ch. 7 - Prob. 8PTB Ch. 7 - Prob. 9PTB Ch. 7 - Prob. 10PTB Ch. 7 - Prob. 11PTB Ch. 7 - Prob. 12PTB Ch. 7 - Prob. 13PTB Ch. 7 - Prob. 14PTB Ch. 7 - Prob. 15PTB Ch. 7 - Prob. 16PTB Ch. 7 - Prob. 17PTB Ch. 7 - Prob. 18PTB Ch. 7 - Prob. 19PTB Ch. 7 - Prob. 20PTB Ch. 7 - Prob. 1CRE Ch. 7 - Prob. 2CRE Ch. 7 - Prob. 3CRE Ch. 7 - Prob. 4CRE Ch. 7 - Prob. 5CRE Ch. 7 - Prob. 6CRE Ch. 7 - Prob. 7CRE Ch. 7 - Prob. 8CRE Ch. 7 - Prob. 9CRE Ch. 7 - Prob. 10CRE Ch. 7 - Prob. 11CRE Ch. 7 - Prob. 12CRE Ch. 7 - Prob. 13CRE Ch. 7 - Prob. 14CRE Ch. 7 - Prob. 15CRE Ch. 7 - Prob. 16CRE Ch. 7 - Prob. 17CRE Ch. 7 - Prob. 18CRE Ch. 7 - Prob. 19CRE Ch. 7 - Prob. 20CRE

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To verify: The matrix A B is an invertible matrix and ( A B ) − 1 = B − 1 A − 1 .

Solution Summary: The author explains that the matrix AB is an invertible matrix.

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To verify:

The matrix AB is an invertible matrix and (AB)−1=B−1A−1.

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Chapter 7 Solutions

To verify: The matrix A B is an invertible matrix and ( A B ) − 1 = B − 1 A − 1 .

Solution Summary: The author explains that the matrix AB is an invertible matrix.

Concept explainers

Videos

To verify: The matrix AB is an invertible matrix and (AB)−1=B−1A−1.

Want to see the full answer?

Chapter 7 Solutions

To verify:

The matrix AB is an invertible matrix and (AB)−1=B−1A−1.