Explanation Approach: The Gauss-Jordan elimination method continues the reduction process on the matrices until the reduced row-echelon form is obtained. A matrix in row-echelon form is in reduced row-echelon form when every column that has a leading 1 has zeroes in every position above and below its leading 1 The reduction is done through the three elementary row operations which are as follows, Interchange of two rows. Multiply a row by a nonzero constant. Add a multiple of a row to another row. Calculation: The given equations is, { 2 x − y + 3 z = 24 2 y − z = 14 7 x − 5 y = 6 The coefficient matrix corresponding to the given equations is [ 2 − 1 3 0 2 − 1 7 − 5 0 ] The augmented matrix is given as, [ 2 − 1 3 ⋮ 24 0 2 − 1 ⋮ 14 7 − 5 0 ⋮ 6 ] Solve the matrix using the three elementary row operations as mentioned in the approach part. Perform the row operation R 1 ↔ R 3 as, [ 2 − 1 3 ⋮ 24 0 2 − 1 ⋮ 14 7 − 5 0 ⋮ 6 ] → [ 7 − 5 0 ⋮ 6 0 2 − 1 ⋮ 14 2 − 1 3 ⋮ 24 ] Perform the row operation R 3 ← R 3 − 2 7 R 1 as, [ 7 − 5 0 ⋮ 6 0 2 − 1 ⋮ 14 2 − 1 3 ⋮ 24 ] → [ 7 − 5 0 ⋮ 6 0 2 − 1 ⋮ 14 0 3 7 3 ⋮ 156 7 ] Perform the row operation R 3 ← R 3 − 3 14 R 2 as, [ 7 − 5 0 ⋮ 6 0 2 − 1 ⋮ 14 0 3 7 3 ⋮ 156 7 ] → [ 7 − 5 0 ⋮ 6 0 2 − 1 ⋮ 14 0 0 45 14 ⋮ 135 7 ] Perform the row operation R 3 ← 14 45 R 3 as, [ 7 − 5 0 ⋮ 6 0

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ISBN: 9781337271073

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 8.1, Problem 76E

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The given system of linear equations {2x−y+3z=242y−z=147x−5y=6.

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Chapter 8.1, Problem 75E

Chapter 8.1, Problem 77E

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The given system of linear equations { 2 x − y + 3 z = 24 2 y − z = 14 7 x − 5 y = 6 .

Solution Summary: The author explains the Gauss-Jordan elimination method, which continues the reduction process on the matrices until the reduced row-echelon form is obtained.

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To solve:

The given system of linear equations {2x−y+3z=242y−z=147x−5y=6.

Want to see the full answer?

Chapter 8 Solutions

The given system of linear equations { 2 x − y + 3 z = 24 2 y − z = 14 7 x − 5 y = 6 .

Solution Summary: The author explains the Gauss-Jordan elimination method, which continues the reduction process on the matrices until the reduced row-echelon form is obtained.

Concept explainers

Videos

To solve: The given system of linear equations {2x−y+3z=242y−z=147x−5y=6.

Want to see the full answer?

Chapter 8 Solutions

To solve:

The given system of linear equations {2x−y+3z=242y−z=147x−5y=6.