Explanation Given Information: The system of equation is, x + y + 6 z = − 1 1 3 x − 1 3 y + 2 3 z = 1 1 2 x + z = 0 Formula Used: Elementary row operations: Type 1: Replacing the row R i by a R i , where a is a nonzero number. Type 2: Replacing the row R i by a R i ± b R j , where a is a nonzero number. Gauss Jordan reduction method: Step 1: First, clear the fractions or decimals by using type 1 operation. Step 2: Select the first nonzero element of the first row as pivot element. Step 3: Use the pivot to clear its column using type 2 operation. Step 4: Select the first nonzero element in the second row a pivot and clear its column. Step 5: Turn all the selected pivot elements into a 1 using operations of type 1. Calculation: Consider the system of equation, x + y + 6 z = − 1 1 3 x − 1 3 y + 2 3 z = 1 1 2 x + z = 0 The augmented matrix for the given system of equations is, [ 1 1 6 − 1 1 3 1 2 − 1 3 0 2 3 1 1 0 ] Apply Gauss Jordan reduction method to get the solution of the given system of equation. Begin by the simplification of the second row and third row. Perform the operations R 2 → 3 R 2 and R 3 → 2 R 3 , [ 1 1 6 − 1 1 3 1 2 − 1 3 0 2 3 1 1 0 ] → [ 1 1 6 − 1 1 1 − 1 0 2 2 3 0 ] Next pivot the first nonzero element of the first row and clears its column. Perform the operations R 2 → R 2 − R 1 and R 3 → R 3 − R 1 , [ 1 1 6 − 1 1 1 − 1 0 2 2 3 0 ] → [ 1 1 6 − 1 0 0 − 2 − 1 − 4 − 4 4 1 ] Next simplify the second row. Perform the operation R 2 → 1 2 R 2 , [ 1 1 6 − 1 0 0 − 2 − 1 − 4 − 4 4 1 ] → [ 1 1 6 − 1 0 0 − 1 − 1 − 2 − 4 2 1 ] Next pivot the first nonzero element of the second row and clear its column

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 4.2, Problem 17E

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To calculate: The solution of the system of equations x+y+6z=−1,13x−13y+23z=1,12x+z=0 by the use of Gauss Jordan row reduction.

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Chapter 4.2, Problem 16E

Chapter 4.2, Problem 18E

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Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - In Exercises 1-6, find three different particular...Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...Ch. 4.1 - In Exercises 7-20, find all solutions of the given...

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The solution of the system of equations x + y + 6 z = − 1 , 1 3 x − 1 3 y + 2 3 z = 1 , 1 2 x + z = 0 by the use of Gauss Jordan row reduction.

Solution Summary: The author calculates the solution of the system of equations using Gauss Jordan row reduction.

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To calculate: The solution of the system of equations x+y+6z=−1,13x−13y+23z=1,12x+z=0 by the use of Gauss Jordan row reduction.

Want to see the full answer?

Chapter 4 Solutions