Explanation Given information: The system of linear equation is { − x + 2 y + z − 3 w = 3 3 x − 4 y + z + w = 9 − x − y + z + w = 0 2 x + y + 4 z − 2 w = 3 . Concept used: The procedure to solve a system of linear equation by Gaussian elimination method as, 1 Write augmented matrix of the system. 2. Use elementary row operation to change the augmented matrix to row-echelon form. 3. Write new system of equations that corresponds the row-echelon form of the augmented matrix and solve by back Substation. The augmented matrix is obtained by writing only the coefficient and constants that appears in the equations. Calculation: The given system of linear equation is { − x + 2 y + z − 3 w = 3 3 x − 4 y + z + w = 9 − x − y + z + w = 0 2 x + y + 4 z − 2 w = 3 . Therefore, the augmented matrix of the system of equations is written as, [ − 1 2 1 − 3 3 3 − 4 1 1 9 − 1 − 1 1 1 0 2 1 4 − 2 3 ] Use the elementary row operation − R 1 → R 1 in the above augmented matrix, then it becomes, [ 1 − 2 − 1 3 − 3 3 − 4 1 1 9 − 1 − 1 1 1 0 2 1 4 − 2 3 ] Use the elementary row operation R 2 − 3 R 1 → R 2 in the above augmented matrix, then it becomes, [ 1 − 2 − 1 3 − 3 0 2 4 − 8 18 − 1 − 1 1 1 0 2 1 4 − 2 3 ] Again use the elementary row operation R 3 + R 1 → R 3 in the above augmented matrix, then it becomes, [ 1 − 2 − 1 3 − 3 0 2 4 − 8 18 0 − 3 0 4 − 3 2 1 4 − 2 3 ] Again use the elementary row operation R 4 − 2 R 1 → R 4 in the above augmented matrix, then it becomes, [ 1 − 2 − 1 3 − 3 0 2 4 − 8 18 0 − 3 0 4 − 3 0 5 6 − 8 9 ] Use the elementary row operation 1 2 R 2 → R 2 in the above augmented matrix, then it becomes, [ 1 − 2 − 1 3 − 3 0 1 2 − 4 9 0 − 3 0 4 − 3 0 5 6 − 8 9 ] Apply the elementary row operation R 3 + 3 R 2 → R 3 in the above augmented matrix, then it becomes, [ 1 − 2 − 1 3 − 3 0 1 2 − 4 9 0 0 6 − 8 24 0 5 6 − 8 9 ] Apply the elementary row operation R 4 − 5 R 2 → R 4 in the above augmented matrix, then it becomes, [ 1 − 2 − 1 3 − 3 0 1 2 − 4 9 0 0 6 − 8 24 0

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ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 6.1, Problem 57E

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The system of linear equations {−x+2y+z−3w=33x−4y+z+w=9−x−y+z+w=02x+y+4z−2w=3.

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Chapter 6.1, Problem 56E

Chapter 6.1, Problem 58E

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Chapter 6 Solutions

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Ch. 6.1 - If a system of linear equations has infinitely...Ch. 6.1 - Write the augmented matrix of the following system...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Dimension of a Matrix State the dimension of the...Ch. 6.1 - Prob. 10E

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The system of linear equations { − x + 2 y + z − 3 w = 3 3 x − 4 y + z + w = 9 − x − y + z + w = 0 2 x + y + 4 z − 2 w = 3 .

Solution Summary: The author describes the procedure to solve a system of linear equation by Gaussian elimination method.

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To solve:

The system of linear equations {−x+2y+z−3w=33x−4y+z+w=9−x−y+z+w=02x+y+4z−2w=3.

Want to see the full answer?

Chapter 6 Solutions

The system of linear equations { − x + 2 y + z − 3 w = 3 3 x − 4 y + z + w = 9 − x − y + z + w = 0 2 x + y + 4 z − 2 w = 3 .

Solution Summary: The author describes the procedure to solve a system of linear equation by Gaussian elimination method.

Videos

To solve: The system of linear equations {−x+2y+z−3w=33x−4y+z+w=9−x−y+z+w=02x+y+4z−2w=3.

Want to see the full answer?

Chapter 6 Solutions

To solve:

The system of linear equations {−x+2y+z−3w=33x−4y+z+w=9−x−y+z+w=02x+y+4z−2w=3.