Explanation Given: The system of linear equations is, { − 3 x + 5 y + 3 z = − 19 3 x + 4 y + 4 z = 8 4 x − 8 y − 6 z = 26 Approach: The Gaussian Elimination with Back-Substitution is as follows. Write the augmented matrix of the system of linear equations. Use elementary row operations to rewrite the augmented matrix in row-echelon form. The elementary row operations are; Interchange of two rows. Multiply a row by a nonzero constant. Add a multiple of a row to another row. Write the system of linear equations corresponding to the matrix in row-echelon form and use back-substitution to find the solution. Calculation: Consider the system of linear equations, { − 3 x + 5 y + 3 z = − 19 3 x + 4 y + 4 z = 8 4 x − 8 y − 6 z = 26 The augmented matrix obtained is, [ − 3 5 3 − 19 3 4 4 8 4 − 8 − 6 26 ] Perform the operation R 1 ↔ R 3 . [ 4 − 8 − 6 26 3 4 4 8 − 3 5 3 − 19 ] Perform the operation R 2 → R 2 − 3 4 R 1 . [ 4 − 8 − 6 26 0 10 17 2 − 23 2 − 3 5 3 − 19 ] Perform the operation R 3 → R 3 + 3 4 R 1 . [ 4 − 8 − 6 26 0 10 17 2 − 23 2 0 − 1 − 3 2 1 2 ] Perform the operation R 3 → R 3 + 1 10 R 2

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Author: Larson

Publisher: CENGAGE L

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Chapter 8.1, Problem 6CP

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The solution of the system {−3x+5y+3z=−193x+4y+4z=84x−8y−6z=26.

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Chapter 8.1, Problem 5CP

Chapter 8.1, Problem 7CP

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The solution of the system { − 3 x + 5 y + 3 z = − 19 3 x + 4 y + 4 z = 8 4 x − 8 y − 6 z = 26 .

Solution Summary: The author explains how the Gaussian Elimination with Back-Substitution solves the system of linear equations.

Videos

To find:

The solution of the system {−3x+5y+3z=−193x+4y+4z=84x−8y−6z=26.

Want to see the full answer?

Chapter 8 Solutions

The solution of the system { − 3 x + 5 y + 3 z = − 19 3 x + 4 y + 4 z = 8 4 x − 8 y − 6 z = 26 .

Solution Summary: The author explains how the Gaussian Elimination with Back-Substitution solves the system of linear equations.

Videos

To find: The solution of the system {−3x+5y+3z=−193x+4y+4z=84x−8y−6z=26.

Want to see the full answer?

Chapter 8 Solutions

To find:

The solution of the system {−3x+5y+3z=−193x+4y+4z=84x−8y−6z=26.