Explanation Procedure used: Creamer’s rule for three variables : Step 1: Find the determinant of the coefficients of the variables, D . Choose to expand down column 2. Step 2: Since D ≠ 0 , continue by determining D x by replacing the first column in D with the system’s constants. Find D y by replacing the second column in D with constants. Find D z by replacing the third column in D with constants. Step 3: Find x = D x D , y = D y D and z = D z D . Step 4: Check the correctness of the solutions. Calculation: The given system of equations are { x + y + z = 4 5 x + 2 y − 3 z = 7 2 x − y − z = 5 . It is known that, the solution of the system of equations { a 1 x + b 1 y + c 1 z = d 1 a 2 x + b 2 y + c 2 z = d 2 a 3 x + b 3 y + c 3 z = d 3 is given by x = D x D , y = D y D and z = D z D . Where, D = | a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 | ≠ 0 , D x = | d 1 b 1 c 1 d 2 b 2 c 2 d 3 b 3 c 3 | , D y = | a 1 d 1 c 1 a 2 d 2 c 2 a 3 d 3 c 3 | and D z = | a 1 b 1 d 1 a 2 b 2 d 2 a 3 b 3 d 3 | Let D = | 1 1 1 5 2 − 3 2 − 1 − 1 | , D x = | 4 1 1 7 2 − 3 5 − 1 − 1 | , D y = | 1 4 1 5 7 − 3 2 5 − 1 | and D z = | 1 1 4 5 2 7 2 − 1 5 | . The value of the determinant D = | 1 1 1 5 2 − 3 2 − 1 − 1 | is computed as follows. D = | 1 1 1 5 2 − 3 2 − 1 − 1 | = 1 | 2 − 3 − 1 − 1 | − 1 | 5 − 3 2 − 1 | + 1 | 5 2 2 − 1 | = 1 [ 2 ( − 1 ) − ( − 1 ) ( − 3 ) ] − 1 [ 5 ( − 1 ) − ( 2 ) 2 ] + 1 [ 5 ( − 1 ) − ( 2 ) ( 2 ) ] = 1 ( − 2 − 3 ) − 1 ( − 5 + 6 ) + 1 ( − 5 − 4 ) Simplify further as, D = 1 ( − 5 ) − 1 ( 1 ) + 1 ( − 9 ) = − 5 − 1 − 9 = − 15 Thus, the value of the determinant D = | 1 1 1 5 2 − 3 2 − 1 − 1 | is –15. Obtain the value of D x as follows. D x = | 4 1 1 7 2 − 3 5 − 1 − 1 | = 4 | 2 − 3 − 1 − 1 | − 1 | 7 − 3 5 − 1 | + 1 | 7 2 5 − 1 | = 4 [ 2 ( − 1 ) − ( − 3 ) ( − 1 ) ] − 1 [ 7 ( − 1 ) − ( − 3 ) ( 5 ) ] + 1 [ 7 ( − 1 ) − ( 2 ) ( 5 ) ] = 4 ( − 2 − 3 ) − 1 ( − 7 + 15 ) + 1 ( − 7 − 10 ) Simplify further as, D x = 4 ( − 5 ) − 1 ( 8 ) + ( − 17 ) = − 20 − 8 − 17 = − 45 Than is, D x = − 45

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ISBN: 9780134556079

Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.

Publisher: Pearson,

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Chapter C.4, Problem 31E

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Chapter C.4, Problem 30E

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Chapter C Solutions

Elementary & Intermediate Algebra

Ch. C.1 - A___ ___ ___ ___ is a grouping of two or more...Ch. C.1 - A____ of a system of equations consists of values...Ch. C.1 - Prob. 3E Ch. C.1 - Prob. 4E Ch. C.1 - Prob. 5E Ch. C.1 - True or False A system of two linear equations...Ch. C.1 - Prob. 7E Ch. C.1 - Prob. 8E Ch. C.1 - Prob. 9E Ch. C.1 - Prob. 10E

Ch. C.1 - Prob. 11E Ch. C.1 - Prob. 12E Ch. C.1 - Prob. 13E Ch. C.1 - Prob. 14E Ch. C.1 - Prob. 15E Ch. C.1 - Prob. 16E Ch. C.1 - 17.While a system of equations is solved, a false...Ch. C.1 - Prob. 18E Ch. C.1 - Prob. 19E Ch. C.1 - Prob. 20E Ch. C.1 - Prob. 21E Ch. C.1 - In Problems 2022, solve the system. Draw a graph...Ch. C.1 - Prob. 23E Ch. C.1 - Prob. 24E Ch. C.1 - Prob. 25E Ch. C.1 - Prob. 26E Ch. C.1 - Prob. 27E Ch. C.1 - Prob. 28E Ch. C.1 - Prob. 29E Ch. C.1 - Prob. 30E Ch. C.1 - Prob. 31E Ch. C.1 - Prob. 32E Ch. C.1 - Prob. 33E Ch. C.1 - Prob. 34E Ch. C.1 - Prob. 35E Ch. C.1 - Prob. 36E Ch. C.1 - In Problems 3542, solve the system of equations...Ch. C.1 - Prob. 38E Ch. C.1 - Prob. 39E Ch. C.1 - Prob. 40E Ch. C.1 - Prob. 41E Ch. C.1 - Prob. 42E Ch. C.1 - Prob. 43E Ch. C.1 - Prob. 44E Ch. C.1 - Prob. 45E Ch. C.1 - Prob. 46E Ch. C.1 - Prob. 47E Ch. C.1 - Prob. 48E Ch. C.1 - Prob. 49E Ch. C.1 - Prob. 50E Ch. C.1 - Prob. 51E Ch. C.1 - Prob. 52E Ch. C.1 - Prob. 53E Ch. C.1 - Prob. 54E Ch. C.1 - Prob. 55E Ch. C.1 - Prob. 56E Ch. C.1 - Prob. 57E Ch. C.1 - Prob. 58E Ch. C.1 - Prob. 59E Ch. C.1 - Prob. 60E Ch. C.1 - Prob. 61E Ch. C.1 - Prob. 62E Ch. C.1 - Prob. 63E Ch. C.1 - Prob. 64E Ch. C.1 - Prob. 65E Ch. C.1 - Prob. 66E Ch. C.1 - Prob. 67E Ch. C.1 - Prob. 68E Ch. C.1 - Prob. 69E Ch. C.1 - Prob. 70E Ch. C.1 - Prob. 71E Ch. C.1 - Prob. 72E Ch. C.1 - Prob. 73E Ch. C.1 - Prob. 74E Ch. C.1 - Prob. 75E Ch. C.1 - Prob. 76E Ch. C.1 - Prob. 77E Ch. C.1 - Prob. 78E Ch. C.1 - Prob. 79E Ch. C.1 - Centroid The medians of a triangle are the line...Ch. C.1 - Prob. 81E Ch. C.1 - Prob. 82E Ch. C.1 - Prob. 83E Ch. C.1 - Prob. 84E Ch. C.1 - In this section, we presented two algebraic...Ch. C.1 - Prob. 86E Ch. C.1 - Prob. 87E Ch. C.1 - In the process of solving a system of linear...Ch. C.1 - Prob. 89E Ch. C.1 - Prob. 90E Ch. C.1 - Prob. 91E Ch. C.1 - Prob. 92E Ch. C.1 - Prob. 93E Ch. C.1 - Prob. 94E Ch. C.1 - Prob. 95E Ch. C.1 - Prob. 96E Ch. C.2 - Prob. 1E Ch. C.2 - A _______ to a system of equations consists of...Ch. C.2 - Prob. 3E Ch. C.2 - Prob. 4E Ch. C.2 - Prob. 5E Ch. C.2 - Prob. 6E Ch. C.2 - Prob. 7E Ch. C.2 - Prob. 8E Ch. C.2 - Prob. 9E Ch. C.2 - Prob. 10E Ch. C.2 - Prob. 11E Ch. C.2 - Prob. 12E Ch. C.2 - Prob. 13E Ch. C.2 - Prob. 14E Ch. C.2 - Prob. 15E Ch. C.2 - Prob. 16E Ch. C.2 - Prob. 17E Ch. C.2 - Prob. 18E Ch. C.2 - Prob. 19E Ch. C.2 - Prob. 20E Ch. C.2 - Prob. 21E Ch. C.2 - Prob. 22E Ch. C.2 - Prob. 23E Ch. C.2 - Prob. 24E Ch. C.2 - Prob. 25E Ch. C.2 - Prob. 26E Ch. C.2 - Prob. 27E Ch. C.2 - Prob. 28E Ch. C.2 - Prob. 29E Ch. C.2 - Prob. 30E Ch. C.2 - Prob. 31E Ch. C.2 - Prob. 32E Ch. C.2 - Prob. 33E Ch. C.2 - Prob. 34E Ch. C.2 - Prob. 35E Ch. C.2 - Prob. 36E Ch. C.2 - Prob. 37E Ch. C.2 - Prob. 38E Ch. C.2 - Prob. 39E Ch. C.2 - Prob. 40E Ch. C.2 - Prob. 41E Ch. C.2 - Prob. 42E Ch. C.2 - Prob. 43E Ch. C.2 - Prob. 44E Ch. C.2 - Prob. 45E Ch. C.2 - Prob. 46E Ch. C.2 - Prob. 47E Ch. C.2 - Prob. 48E Ch. C.2 - Prob. 49E Ch. C.2 - Prob. 50E Ch. C.2 - Prob. 51E Ch. C.2 - Prob. 52E Ch. C.2 - Prob. 53E Ch. C.2 - Prob. 54E Ch. C.2 - Prob. 55E Ch. C.2 - Prob. 56E Ch. C.2 - Prob. 57E Ch. C.2 - Prob. 58E Ch. C.2 - Prob. 59E Ch. C.3 - Prob. 1E Ch. C.3 - Prob. 2E Ch. C.3 - Prob. 3E Ch. C.3 - Prob. 4E Ch. C.3 - Prob. 5E Ch. C.3 - Prob. 6E Ch. C.3 - Prob. 7E Ch. C.3 - Prob. 8E Ch. C.3 - Prob. 9E Ch. C.3 - Prob. 10E Ch. C.3 - Prob. 11E Ch. C.3 - Prob. 12E Ch. C.3 - Prob. 13E Ch. C.3 - In Problems 13 and 14, solve each system of...Ch. C.3 - Prob. 15E Ch. C.3 - Prob. 16E Ch. C.3 - Prob. 17E Ch. C.3 - Prob. 18E Ch. C.3 - Prob. 19E Ch. C.3 - Prob. 20E Ch. C.3 - Prob. 21E Ch. C.3 - Prob. 22E Ch. C.3 - Prob. 23E Ch. C.3 - Prob. 24E Ch. C.3 - Prob. 25E Ch. C.3 - Prob. 26E Ch. C.3 - Prob. 27E Ch. C.3 - Prob. 28E Ch. C.3 - Prob. 29E Ch. C.3 - Prob. 30E Ch. C.3 - Prob. 31E Ch. C.3 - Prob. 32E Ch. C.3 - Prob. 33E Ch. C.3 - Prob. 34E Ch. C.3 - Prob. 35E Ch. C.3 - Prob. 36E Ch. C.3 - Prob. 37E Ch. C.3 - Prob. 38E Ch. C.3 - Prob. 39E Ch. C.3 - Prob. 40E Ch. C.3 - Prob. 41E Ch. C.3 - In Problems 39-44, solve each system of equations...Ch. C.3 - Prob. 43E Ch. C.3 - Prob. 44E Ch. C.3 - Prob. 45E Ch. C.3 - Prob. 46E Ch. C.3 - Prob. 47E Ch. C.3 - Prob. 48E Ch. C.3 - Prob. 49E Ch. C.3 - Prob. 50E Ch. C.3 - Prob. 51E Ch. C.3 - Prob. 52E Ch. C.3 - Prob. 53E Ch. C.3 - Prob. 54E Ch. C.3 - In Problems 51-56, an augmented matrix of a system...Ch. C.3 - In Problems 51-56, an augmented matrix of a system...Ch. C.3 - Prob. 57E Ch. C.3 - Prob. 58E Ch. C.3 - Prob. 59E Ch. C.3 - Prob. 60E Ch. C.3 - Prob. 61E Ch. C.3 - Prob. 62E Ch. C.3 - Prob. 63E Ch. C.3 - Prob. 64E Ch. C.3 - Prob. 65E Ch. C.3 - Prob. 66E Ch. C.3 - In Problems 57-78, solve each system of equations...Ch. C.3 - Prob. 68E Ch. C.3 - Prob. 69E Ch. C.3 - Prob. 70E Ch. C.3 - Prob. 71E Ch. C.3 - Prob. 72E Ch. C.3 - Prob. 73E Ch. C.3 - Prob. 74E Ch. C.3 - Prob. 75E Ch. C.3 - Prob. 76E Ch. C.3 - Prob. 77E Ch. C.3 - In Problems 45-50, solve each system of equations...Ch. C.3 - Prob. 79E Ch. C.3 - Prob. 80E Ch. C.3 - Finance Carissa has 20,000 to invest. Her...Ch. C.3 - Prob. 82E Ch. C.3 - Prob. 83E Ch. C.3 - Prob. 84E Ch. C.3 - Prob. 85E Ch. C.3 - Prob. 86E Ch. C.3 - Prob. 87E Ch. C.3 - Prob. 88E Ch. C.3 - Prob. 89E Ch. C.3 - Prob. 90E Ch. C.3 - Graphing calculators have the ability to solve...Ch. C.3 - Prob. 92E Ch. C.3 - Prob. 93E Ch. C.3 - Graphing calculators have the ability to solve...Ch. C.4 - D = |abcd| = _____________.Ch. C.4 - Prob. 2E Ch. C.4 - Prob. 3E Ch. C.4 - Prob. 4E Ch. C.4 - Prob. 5E Ch. C.4 - In Problems 5 and 6, use Cramers Rule to solve the...Ch. C.4 - Prob. 7E Ch. C.4 - Prob. 8E Ch. C.4 - Prob. 9E Ch. C.4 - Prob. 10E Ch. C.4 - Prob. 11E Ch. C.4 - Prob. 12E Ch. C.4 - Prob. 13E Ch. C.4 - Prob. 14E Ch. C.4 - Prob. 15E Ch. C.4 - Prob. 16E Ch. C.4 - Prob. 17E Ch. C.4 - Prob. 18E Ch. C.4 - In Problems 15-22, solve each system of equations...Ch. C.4 - Prob. 20E Ch. C.4 - Prob. 21E Ch. C.4 - Prob. 22E Ch. C.4 - Prob. 23E Ch. C.4 - Prob. 24E Ch. C.4 - Prob. 25E Ch. C.4 - Prob. 26E Ch. C.4 - Prob. 27E Ch. C.4 - Prob. 28E Ch. C.4 - Prob. 29E Ch. C.4 - Prob. 30E Ch. C.4 - Prob. 31E Ch. C.4 - Prob. 32E Ch. C.4 - Prob. 33E Ch. C.4 - Prob. 34E Ch. C.4 - Prob. 35E Ch. C.4 - Prob. 36E Ch. C.4 - Prob. 37E Ch. C.4 - Prob. 38E Ch. C.4 - Prob. 39E Ch. C.4 - Prob. 40E Ch. C.4 - Prob. 41E Ch. C.4 - Prob. 42E Ch. C.4 - Prob. 43E Ch. C.4 - Prob. 44E Ch. C.4 - Prob. 45E Ch. C.4 - Prob. 46E Ch. C.4 - Prob. 47E Ch. C.4 - Prob. 48E Ch. C.4 - Problems 4750, use the following result....Ch. C.4 - Prob. 50E Ch. C.4 - Prob. 51E Ch. C.4 - Prob. 52E Ch. C.4 - Prob. 53E Ch. C.4 - Prob. 54E Ch. C.4 - Prob. 55E Ch. C.4 - In Problems 5560, use technology to solve the...Ch. C.4 - Prob. 57E Ch. C.4 - In Problems 5560, use technology to solve the...Ch. C.4 - Prob. 59E Ch. C.4 - Prob. 60E

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The system of given linear equations by using the Cramers rule.

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Chapter C Solutions