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 − 5 y = 4 x + y − z = 8 3 x + 5 z = 0 . The matrix D is the coefficient matrix. | D | = | 2 − 5 0 1 1 − 1 3 0 5 | = 2 | 1 − 1 0 5 | + 5 | 1 − 1 3 5 | + 0 = 2 ( 5 − 0 ) + 5 ( 5 + 3 ) = 50 … ( 1 ) The matrix D x is obtained by replacing the first columns of D by the constant terms. | D x | = | 4 − 5 0 8 1 − 1 0 0 5 | = 4 | 1 − 1 0 5 | − ( − 5 ) | 8 − 1 0 5 | + 0 = 4 ( 5 − 0 ) + 5 ( 40 ) = 220 … ( 2 ) The matrix D y is obtained by replacing the second columns of D by the constant terms. | D y | = | 2 4 0 1 8 − 1 3 0 5 | = 2 | 8 − 1 0 5 | − 4 | 1 − 1 3 5 | + 0 = 2 ( 40 ) − 4 ( 5 + 3 ) = 48 … ( 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 11.4, Problem 54E

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The system of equation {2x−5y =4x+y−z=83x +5z=0 using Cramer’s rule.

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Chapter 11.4, Problem 53E

Chapter 11.4, Problem 55E

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The system of equation { 2 x − 5 y = 4 x + y − z = 8 3 x + 5 z = 0 using Cramer’s rule.

Solution Summary: The author explains the Cramer's rule for the system of equations c2x-5y

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To solve:

The system of equation {2x−5y =4x+y−z=83x +5z=0 using Cramer’s rule.

Want to see the full answer?

Chapter 11 Solutions

The system of equation { 2 x − 5 y = 4 x + y − z = 8 3 x + 5 z = 0 using Cramer’s rule.

Solution Summary: The author explains the Cramer's rule for the system of equations c2x-5y

Videos

To solve: The system of equation {2x−5y =4x+y−z=83x +5z=0 using Cramer’s rule.

Want to see the full answer?

Chapter 11 Solutions

To solve:

The system of equation {2x−5y =4x+y−z=83x +5z=0 using Cramer’s rule.