Explanation Given: The system of equations is, 4 x − y + z = 12 2 x + 2 y + 3 z = 1 5 x − 2 y + 6 z = 22... ( 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 = | 4 − 1 1 2 2 3 5 − 2 6 | = 4 ( 12 − ( − 6 ) ) − ( − 1 ) ( 12 − 15 ) + 1 ( − 4 − 10 ) = 72 − 3 − 14 = 55 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 = | 12 − 1 1 1 2 3 22 − 2 6 | = 12 ( 12 − ( − 6 ) ) − ( − 1 ) ( 6 − 66 ) + 1 ( − 2 − 44 ) = 216 − 60 − 46 = 110 Substitute 110 for D x and 55 for D in equation ( 2 )

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Author: Ron Larson

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Chapter 8.5, Problem 2CP

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The system of equation 4x−y+z=122x+2y+3z=15x−2y+6z=22 with the Cramer’s rule.

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Chapter 8.5, Problem 1CP

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The system of equation 4 x − y + z = 12 2 x + 2 y + 3 z = 1 5 x − 2 y + 6 z = 22 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 4x−y+z=122x+2y+3z=15x−2y+6z=22 with the Cramer’s rule.

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Chapter 8 Solutions

The system of equation 4 x − y + z = 12 2 x + 2 y + 3 z = 1 5 x − 2 y + 6 z = 22 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 4x−y+z=122x+2y+3z=15x−2y+6z=22 with the Cramer’s rule.

Want to see the full answer?

Chapter 8 Solutions

To solve:

The system of equation 4x−y+z=122x+2y+3z=15x−2y+6z=22 with the Cramer’s rule.