Explanation Given Information: The provided system of equations are, 4 x − 2 y + 6 z = 2 − 6 x + 3 y − 9 z = − 3 2 x − 7 y + 11 z = − 5 Formula Used: The Cramer’s rule to solve system of the equation is as follows: The standard form of the system of equation in three variable x , y and z is given by, 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 The determinant D is obtained by using coefficient of the variables in the form D = | a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 | , The determinant D x is obtained by replacing a 1 , a 2 , a 3 by d 1 , d 2 , d 3 respectively in determinant D , that is D x = | d 1 b 1 c 1 d 2 b 2 c 2 d 3 b 3 c 3 | . Similarly D y is obtained by replacing b 1 , b 2 , b 3 by d 1 , d 2 , d 3 respectively in determinant D , that is D y = | a 1 d 1 c 1 a 2 d 2 c 2 a 3 d 3 c 3 | And D z is obtained by replacing c 1 , c 2 , c 3 by d 1 , d 2 , d 3 respectively in determinant D , that is D z = | a 1 b 1 d 1 a 2 b 2 d 2 a 3 b 3 d 3 | The variables x , y and z are computed as, x = D x D , y = D y D and z = D z D , provided D ≠ 0 Case 1: If D = 0 and either of D x ≠ 0 , D y ≠ 0 or D z ≠ 0 then the system of equation is inconsistent and has no solution. Case 2: If D = 0 and D x = 0 , D y = 0 , D z = 0 then the system of equations is dependent and has infinitely many solutions. Where the value of a determinant is calculated as follows: If expansion is with the minor determinant of first column, then, A = | a d g b e h c f i | = a | e h f i | − b | d g f i | + c | d g e h | = a ( e i − f h ) − b ( d i − f g ) + c ( d h − e g ) Calculation: Consider the provided system of equations, 4 x − 2 y + 6 z = 2 − 6 x + 3 y − 9 z = − 3 2 x − 7 y + 11 z = − 5 Compare the equations 4 x − 2 y + 6 z = 2 − 6 x + 3 y − 9 z = − 3 2 x − 7 y + 11 z = − 5 with standard form 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 , this gives, a 1 = 4 , b 1 = − 2 , c 1 = 6 , d 1 = 2 a 2 = − 6 , b 2 = 3 , c 2 = − 9 , d 2 = − 3 a 3 = 2 , b 3 = − 7 , c 3 = 11 , d 3

Intermediate Algebra For College Students (9th Edition)

9th Edition

ISBN: 9780321927354

Author: Allen R. Angel, Dennis Runde

Publisher: PEARSON

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Chapter 4.5, Problem 40ES

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To calculate: The solution of the system of equations 4x−2y+6z=2−6x+3y−9z=−32x−7y+11z=−5 by using determinants.

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Chapter 4.5, Problem 39ES

Chapter 4.5, Problem 41ES

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The solution of the system of equations 4 x − 2 y + 6 z = 2 − 6 x + 3 y − 9 z = − 3 2 x − 7 y + 11 z = − 5 by using determinants.

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To calculate: The solution of the system of equations 4x−2y+6z=2−6x+3y−9z=−32x−7y+11z=−5 by using determinants.

Want to see the full answer?

Chapter 4 Solutions