Explanation Given: The system of equations is, x + 2 y + 3 z = − 3 − 2 x + y − z = 6 3 x − 3 y + 2 z = − 11... ( 1 ) Approach: In the Cramer’s Rule, if a system of n linear equations in n variables has a coefficient matrix A with a nonzero determinant | A | , then the solution of the system is, x 1 = | A 1 | | A | , x 2 = | A 2 | | A | , x 3 = | A 3 | | A | Here, the i th column of A i is the column of constants in the system of equations. If the determinant of the coefficient matrix is zero, then the system has either no solutions or infinitely many solutions. Calculation: The determinant of the coefficient matrix for the system of linear equations is, D = | 1 2 3 − 2 1 − 1 3 − 3 2 | = 1 ( 2 − 3 ) − ( 2 ) ( − 4 − ( − 3 ) ) + 3 ( 6 − 3 ) = − 1 + 2 + 9 = 10 The determinant is nonzero so, Cramer’s Rule can be applied. The solution for x is given by, x = D x D ... ( 2 ) The solution for y is given by, y = D y D ... ( 3 ) The solution for z is given by, z = D z D ... ( 4 ) The determinant D x is, D x = | − 3 2 3 6 1 − 1 − 11 − 3 2 | = − 3 ( 2 − 3 ) − ( 2 ) ( 12 − 11 ) + 3 ( − 18 + 11 ) = 3 − 2 − 21 = − 20 Substitute − 20 for D x and 10 for D in equation ( 2 )

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Author: Ron Larson

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Chapter 8.5, Problem 13E

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The system of equation {x+2y+3z=−3−2x+y−z=63x−3y+2z=−11 with the Cramer’s rule.

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Chapter 8.5, Problem 12E

Chapter 8.5, Problem 14E

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Ch. 8.1 - Prob. 1CP Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Prob. 5CP Ch. 8.1 - Prob. 6CP Ch. 8.1 - Prob. 7CP Ch. 8.1 - Prob. 8CP Ch. 8.1 - Prob. 9CP Ch. 8.1 - Prob. 1E

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The system of equation { x + 2 y + 3 z = − 3 − 2 x + y − z = 6 3 x − 3 y + 2 z = − 11 with the Cramer’s rule.

Solution Summary: The author explains the Cramer's rule for the solution of the system of linear equations in n variables.

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To solve:

The system of equation {x+2y+3z=−3−2x+y−z=63x−3y+2z=−11 with the Cramer’s rule.

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Chapter 8 Solutions

The system of equation { x + 2 y + 3 z = − 3 − 2 x + y − z = 6 3 x − 3 y + 2 z = − 11 with the Cramer’s rule.

Solution Summary: The author explains the Cramer's rule for the solution of the system of linear equations in n variables.

Videos

To solve: The system of equation {x+2y+3z=−3−2x+y−z=63x−3y+2z=−11 with the Cramer’s rule.

Want to see the full answer?

Chapter 8 Solutions

To solve:

The system of equation {x+2y+3z=−3−2x+y−z=63x−3y+2z=−11 with the Cramer’s rule.