Explanation Given Information: The provided system of equations is, 3 x − y − z = 0 x + y + z = 4 Formula Used: Elementary row operations: Type 1: Replace the row R i by a R i , where a is a nonzero real number. Type 2: Replace the row R i by a R i ± b R j , where a and b is a nonzero real number. Gauss Jordan reduction method: Step 1: First clear the fractions or decimals if any, using operations of type 1. Step 2: Select the first nonzero element of the first row as a pivot. Step 3: Make all elements below and above the pivot element zero in that column zero using operations of type 2. 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 1 using operations of type 1. Calculation: Consider the provided system of equations, 3 x − y − z = 0 x + y + z = 4 The augmented matrix for the given system of equations is, [ 3 − 1 − 1 0 1 1 1 4 ] Apply Gauss Jordan reduction method to get the solution of the given system of equations. Begin by the selection of the first nonzero element of the first row and clear its column. The pivot element in the first row is 3. [ 3 − 1 − 1 0 1 1 1 4 ] Perform the operation R 2 → 3 R 2 − R 1 , [ 3 − 1 − 1 0 1 1 1 4 ] → [ 3 − 1 − 1 0 0 4 4 12 ] Next, simplify the second row. The pivot element in the second row is 4

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 26E

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To calculate: The solution of the given system of equations 3x−y−z=0,x+y+z=4 by the use of Gauss Jordan row reduction.

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Chapter 4.2, Problem 25E

Chapter 4.2, Problem 27E

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Chapter 4 Solutions

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 given system of equations 3 x − y − z = 0 , x + y + z = 4 by the use of Gauss Jordan row reduction.

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To calculate: The solution of the given system of equations 3x−y−z=0,x+y+z=4 by the use of Gauss Jordan row reduction.

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Chapter 4 Solutions