Explanation Given information: The linear system of equations is, { − 2 a + c = 2 a + 2 b − c = 9 3 a + 5 b + 2 c = 22 Formula used : The general linear system of equations can be expressed as, { a 11 x + a 12 y + a 13 z = r a 21 x + a 22 y + a 23 z = s a 31 x + a 32 y + a 33 z = t The solution of the above system of equation can be calculated as, x = | D x | | D | , y = | D y | | D | and z = | D z | | D | Here, the determinant | D | = | a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 | ≠ 0 . The matrices D , D x , D y and D z are represented as follows, D = [ a 11 a 12 a 13 a 21 a 22 a 23 a 31 a 32 a 33 ] , D x = [ r a 12 a 13 s a 22 a 23 t a 32 a 33 ] D y = [ a 11 r a 13 a 21 s a 23 a 31 t a 33 ] and D z = [ a 11 a 12 r a 21 a 22 s a 31 a 32 t ] Calculation: The system of equations is { − 2 a + c = 2 a + 2 b − c = 9 3 a + 5 b + 2 c = 22 . For the system of equations, the coefficient matrix can be obtained as, D = [ 5 − 3 1 0 4 − 6 7 10 0 ] The determinant of the coefficient matrix D can be calculated as, | D | = | − 2 0 1 1 2 − 1 3 5 2 | = − 2 ( 2 ⋅ 2 − ( − 1 ) ⋅ 5 ) + 0 ( 1 ⋅ 2 − ( − 1 ) ⋅ 3 ) + 1 ( 1 ⋅ 5 − 2 ⋅ 3 ) = − 2 ( 4 + 5 ) + 0 + 1 ( 5 − 6 ) = − 19 The matrix D a can be obtained by replacing the first column of the matrix by the values of the equations or the constants 2 , 9 , 22 as, D a = [ 2 0 1 9 2 − 1

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ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 6.4, Problem 50E

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The system of equations {−2a+c=2a+2b−c=93a+5b+2c=22 by the Cramer’s rule.

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Chapter 6.4, Problem 49E

Chapter 6.4, Problem 51E

Chapter 6 Solutions

College Algebra

Ch. 6.1 - If a system of linear equations has infinitely...Ch. 6.1 - Write the augmented matrix of the following system...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Dimension of a Matrix State the dimension of the...Ch. 6.1 - Prob. 10E

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The system of equations { − 2 a + c = 2 a + 2 b − c = 9 3 a + 5 b + 2 c = 22 by the Cramer’s rule.

Solution Summary: The author explains how the linear system of equations is solved by the Cramer's rule.

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To solve:

The system of equations {−2a+c=2a+2b−c=93a+5b+2c=22 by the Cramer’s rule.

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Chapter 6 Solutions

The system of equations { − 2 a + c = 2 a + 2 b − c = 9 3 a + 5 b + 2 c = 22 by the Cramer’s rule.

Solution Summary: The author explains how the linear system of equations is solved by the Cramer's rule.

Videos

To solve: The system of equations {−2a+c=2a+2b−c=93a+5b+2c=22 by the Cramer’s rule.

Want to see the full answer?

Chapter 6 Solutions

To solve:

The system of equations {−2a+c=2a+2b−c=93a+5b+2c=22 by the Cramer’s rule.