Explanation Given information: The system of equations is { 2 x − y + 5 z = 0 − x + 7 y = 9 5 x + 4 y + 3 z = − 9 . Concept used: Matrix equation for system of equations: For a system of equations { a x + b y + c z = m d x + e y + f z = n g x + h y + i z = o , the corresponding matrix equation is given by, [ a b c d e f g h i ] [ x y z ] = [ m n o ] ...... (1) Here, [ a b c d e f g h i ] is the coefficient matrix, [ x y z ] is the variable matrix and [ m n o ] is the known matrix. Cramer’s rule: If a system of n linear equations in the n variables x 1 , x 2 , x 3 , … , x n is equivalent to the matrix equation D X = B , and if | D | ≠ 0 , then its solutions are, x 1 = | D x 1 | | D | , x 2 = | D x 2 | | D | , … , x n = | D x n | | D | Here, D x i is the matrix obtained by replacing the ith column of D by the n × 1 matrix B. Calculation: The given system of equation is written in the form of matrix equation as follows. [ 2 − 1 5 − 1 7 0 5 4 3 ] [ x y z ] = [ 0 9 − 9 ] Compare the above matrix equation with the equation (1) to obtain the coefficient matrix A and matrix B as, A = [ 2 − 1 5 − 1 7 0 5 4 3 ] B = [ 0 9 − 9 ] In the given system of equations, there are two variables x and y therefore two matrix D x and D y are to be obtained. Hence by the Cramer’s rule, the value of variable x is, x = | D x | | D | ...... (2) Similarly, the value of variable y is, y = | D y | | D | ...... (3) Similarly, the value of variable z is, z = | D z | | D | ...... (4) The determinant | D | of the coefficient matrix is calculated as, | D | = | 2 − 1 5 − 1 7 0 5 4 3 | = 2 ( 21 − 0 ) + 1 ( − 3 − 0 ) + 5 ( − 4 − 35 ) = 24 − 3 − 195 = − 174 Now, the value of | D x | is calculated as shown below

Bundle: College Algebra, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's College Algebra, 7th Edition, Single-Term

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ISBN: 9781305718944

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 6, Problem 69E

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

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Chapter 6, Problem 68E

Chapter 6, Problem 70E

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Bundle: College Algebra, 7th + WebAssign Printed Access Card for Stewart/Redlin/Watson's College Algebra, 7th Edition, Single-Term

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The solution of system of equations { 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 how Cramer's rule solves the system of equations c2x-y+5z=0 -x+7y=9

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To find:

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

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Chapter 6 Solutions

The solution of system of equations { 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 how Cramer's rule solves the system of equations c2x-y+5z=0 -x+7y=9

Videos

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

Want to see the full answer?

Chapter 6 Solutions

To find:

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