Explanation Given Information: The system of equations: 3 x − 2 y + z = 16 2 x + 3 y − z = − 9 x + 4 y + 3 z = 2 Formula used: For a system of equations a 1 x + b 1 y + c 1 z = d 1 , a 2 x + b 2 y + c 2 z = d 2 and a 3 x + b 3 y + c 3 z = d 3 , the solution to the system of equations by Cramer’s Rule is defined as, x = D x D , y = D y D and z = D z D Here, D = | a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 | ≠ 0 , D x = | d 1 b 1 c 1 d 2 b 2 c 2 d 3 b 3 c 3 | , D y = | a 1 d 1 c 1 a 2 d 2 c 2 a 3 d 3 c 3 | and D z = | a 1 b 1 d 1 a 2 b 2 d 2 a 3 b 3 d 3 | Calculation: Consider the system of equations, 3 x − 2 y + z = 16 2 x + 3 y − z = − 9 x + 4 y + 3 z = 2 The determinant of the provided system of equations can be calculated as: Use the formula | a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 | = a 1 | b 2 c 2 b 3 c 3 | − a 2 | b 1 c 1 b 3 c 3 | + a 3 | b 1 c 1 b 2 c 2 | to evaluate the determinant. Therefore, | 3 − 2 1 2 3 − 1 1 4 3 | = 3 | 3 − 1 4 3 | − 2 | − 2 1 4 3 | + 1 | − 2 1 3 − 1 | = 3 ( 3 ⋅ 3 − 4 ⋅ ( − 1 ) ) − 2 ( ( − 2 ) ⋅ 3 − 4 ⋅ 1 ) + 1 ( ( − 2 ) ( − 1 ) − 3 ⋅ 1 ) = 3 ( 9 + 4 ) − 2 ( − 6 − 4 ) + 1 ( 2 − 3 ) = 3 ( 13 ) − 2 ( − 10 ) + 1 ( − 1 ) Multiply to clear parenthesis and simplify, | 3 − 2 1 2 3 − 1 1 4 3 | = 39 + 20 − 1 = 58 So, the value of the determinant is D = 58 . As the determinant value is not zero, Cramer’s Rule can be used to solve the system

Precalculus, Books A La Carte Edition Plus MyLab Math with eText -- Access Card Package (6th Edition)

6th Edition

ISBN: 9780134765471

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 8.5, Problem 5CP

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To calculate: The solution of the system 3x−2y+z=16,2x+3y−z=−9 and x+4y+3z=2 by the use of Cramer’s Rule.

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Chapter 8.5, Problem 4CP

Chapter 8.5, Problem 6CP

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Chapter 8 Solutions

Precalculus, Books A La Carte Edition Plus MyLab Math with eText -- Access Card Package (6th Edition)

Ch. 8.1 - Check Point 1 Write the augmented matrix for the...Ch. 8.1 - Check Point 2 Use the matrix ...Ch. 8.1 - Check Point 3 Use matrices to solve the system:...Ch. 8.1 - Check Point 4 Use matrices to solve the system:...Ch. 8.1 - Check Point 5 Solve the system in Check Point. 3...Ch. 8.1 - Prob. 1CVC Ch. 8.1 - Fill in each blank so that the resulting statement...Ch. 8.1 - Prob. 3CVC Ch. 8.1 - Prob. 4CVC Ch. 8.1 - Fill in each blank so that the resulting statement...

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The solution of the system 3 x − 2 y + z = 16 , 2 x + 3 y − z = − 9 and x + 4 y + 3 z = 2 by the use of Cramer’s Rule.

Solution Summary: The author calculates the solution of the system 3x-2y+z by the use of Cramer’s Rule.

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To calculate: The solution of the system 3x−2y+z=16,2x+3y−z=−9 and x+4y+3z=2 by the use of Cramer’s Rule.

Want to see the full answer?

Chapter 8 Solutions