Explanation Given Information: System of linear equations is: { x + y + 2 w = 4 x + 2 y + 2 z = 7 2 x + y − z + 6 w = 5 − x + y + 2 z − 6 w = 2 Formula used: Gauss Jordan Elimination Method: The following elementary row operations may be performed on an augmented matrix to get reduced row echelon form: Step1: Establish an augmented matrix from the system of linear equations. Step2: Find the first column from the left with a non-zero entry and move the row comprising that entry to the top of the rows being operated. Step3: Using the first element in the first column, pivot the matrix. Step4: Find the second column from the left with a non-zero entry and move the row comprising that element to the second entry. Step5: Using the second element in the second column, pivot the matrix. Step6: Continue this process until the diagonal form is attained. Step7: Write the answer in the form of linear equations equivalent to the matrix. Calculation: Consider the system of linear equations, { x + y + 2 w = 4 x + 2 y + 2 z = 7 2 x + y − z + 6 w = 5 − x + y + 2 z − 6 w = 2 From the systems of linear equation, the augmented matrix is [ 1 1 0 2 4 1 2 2 0 7 2 1 − 1 6 5 − 1 1 2 − 6 2 ] . Pivot the matrix about the boxed element as follows: Transform 1 into 0 by multiplying row 1 by − 1 and adding the result into row 2 . Transform 2 into 0 by multiplying row 1 by − 2 and adding the result into row 3 . Transform − 1 into 0 by multiplying row 1 by 1 and adding the result into row 4 . [ 1 1 0 2 4 1 2 2 0 7 2 1 − 1 6 5 − 1 1 2 − 6 2 ] → R 2 + ( − 1 ) R 1 R 3 + ( − 2 ) R 1 R 4 + ( 1 ) R 1 [ 1 1 0 2 4 0 1 2 − 2 3 0 − 1 − 1 2 − 3 0 2 2 − 4 6 ] Transform 1 into 0 by multiplying row 2 by − 1 and adding the result into row 1

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 2.2, Problem 36E

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To calculate: The solution to the system of linear equations { x+ y +2w=4 x+ 2y+2z=72x+ y− z +6w=5−x+ y+2z−6w=2 using the Gauss-Jorden elimination method.

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Chapter 2.2, Problem 35E

Chapter 2.2, Problem 37E

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Chapter 2 Solutions

Finite Mathematics & Its Applications (12th Edition)

Ch. 2.1 - 1. Determine whether the following systems of...Ch. 2.1 - Give the meaning of each of the following...Ch. 2.1 - 3. Perform the indicated elementary row...Ch. 2.1 - State the next elementary row operation that...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - Prob. 2E Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 1–8, perform the indicated elementary...Ch. 2.1 - In Exercises 18, perform the indicated elementary...Ch. 2.1 - In Exercises 18, perform the indicated elementary...

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The solution to the system of linear equations { x + y + 2 w = 4 x + 2 y + 2 z = 7 2 x + y − z + 6 w = 5 − x + y + 2 z − 6 w = 2 using the Gauss-Jorden elimination method.

Solution Summary: The author explains the Gauss-Jorden elimination method to calculate the solution to the system of linear equations.

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To calculate: The solution to the system of linear equations { x+ y +2w=4 x+ 2y+2z=72x+ y− z +6w=5−x+ y+2z−6w=2 using the Gauss-Jorden elimination method.

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Chapter 2 Solutions