Explanation Approach: The Cramer’s rule for the system in three variables is given below, If a system of n linear equations in the n variable x 1 , x 2 ,…, x n is equivalent to the matrix equation D X = B , and if | D | ≠ 0 , then its solutions are given below. x 1 = | D x 1 | | D | , x 2 = | D x 2 | | D | ,………, x n = | D x n | | D | The matrix D x i is obtained by replacing the i t h column of D by the n × 1 matrix B . Calculation: Consider the system of equations { 2 x − y + 5 z = 0 − x + 7 y = 9 5 x + 4 y + 3 z = − 9 . The matrix D is the coefficient matrix. | D | = | 2 − 1 5 − 1 7 0 5 4 3 | = 2 | 7 0 4 3 | − ( − 1 ) | − 1 0 5 3 | + 5 | − 1 7 5 4 | = 42 − 3 − 195 = − 156 …… ( 1 ) The matrix D x is obtained by replacing the first columns of D by the constant terms. | D x | = | 0 − 1 5 9 7 0 − 9 4 3 | = 0 − ( − 1 ) | 9 0 − 9 3 | + 5 | 9 7 − 9 4 | = 0 + 27 + 495 = 522 …… ( 2 ) The matrix D y is obtained by replacing the second columns of D by the constant terms. | D y | = | 2 0 5 − 1 9 0 5 − 9 3 | = 2 | 9 0 − 9 3 | − 0 + 5 | − 1 9 5 − 9 | = 54 − 0 + − 180 = − 126 …… ( 3 ) The matrix D z is obtained by replacing the third columns of D by the constant terms

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ISBN: 9781305719781

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: PEARSON

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Chapter 11.CR, Problem 69E

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The system of equation {2x−y+5z=0−x+7y=95x+4y+3z=−9 using Cramer’s rule.

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Chapter 11.CR, Problem 68E

Chapter 11.CR, Problem 70E

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The system of equation { 2 x − y + 5 z = 0 − x + 7 y = 9 5 x + 4 y + 3 z = − 9 using Cramer’s rule.

Solution Summary: The author explains the Cramer's rule for the system of equations c2x-y+5z=0 -x+7y=9 5

Videos

To solve:

The system of equation {2x−y+5z=0−x+7y=95x+4y+3z=−9 using Cramer’s rule.

Want to see the full answer?

Chapter 11 Solutions

The system of equation { 2 x − y + 5 z = 0 − x + 7 y = 9 5 x + 4 y + 3 z = − 9 using Cramer’s rule.

Solution Summary: The author explains the Cramer's rule for the system of equations c2x-y+5z=0 -x+7y=9 5

Videos

To solve: The system of equation {2x−y+5z=0−x+7y=95x+4y+3z=−9 using Cramer’s rule.

Want to see the full answer?

Chapter 11 Solutions

To solve:

The system of equation {2x−y+5z=0−x+7y=95x+4y+3z=−9 using Cramer’s rule.