Explanation Given information: The system of equations is written as, x + y + z + w = 0 x − y − 4 z − w = − 1 x − 2 y + 4 w = − 7 2 x + 2 y + 3 z + 4 w = − 3 Concept used: If the system of equation is given as follows, a 11 x + a 12 y + a 13 z + a 14 w = b 1 a 21 x + a 22 y + a 23 z + a 24 w = b 2 a 31 x + a 32 y + a 33 z + a 34 w = b 3 a 41 x + a 42 y + a 43 z + a 44 w = b 4 Then, the augmented matrix is written as, A augmented = [ a 11 a 12 a 13 a 14 b 1 a 21 a 22 a 23 a 24 b 2 a 31 a 32 a 33 a 34 b 3 a 41 a 42 a 43 a 44 b 4 ] The Gauss Elimination method states that any system of equations can be written in the form of an augmented matrix, which is then transformed to row-echelon form by elementary row transformation and then the last row of the row-echelon matrix is back substituted to its previous rows to find the complete solution of the given system of equations Conditions for matrix to be in row-echelon form are as follows, The first non-zero entry (Leading entry) in each row should be 1 . The leading entry of each row is to the right of the leading entry in the row above it. Rows with all elements as zero must be at the bottom of the matrix. Calculation: The augmented matrix can be written as, A = [ 1 1 1 1 0 1 − 1 − 4 − 1 − 1 1 − 2 0 4 − 7 2 2 3 4 − 3 ] Apply row transformations R 2 − R 1 → R 2 to reduce it to the row-echelon form as, A = [ 1 1 1 1 0 0 − 2 − 5 − 2 − 1 1 − 2 0 4 − 7 2 2 3 4 − 3 ] Apply row transformations R 3 − R 1 → R 3 to reduce it to the row-echelon form as, A = [ 1 1 1 1 0 0 − 2 − 5 − 2 − 1 0 − 3 − 1 3 − 7 2 2 3 4 − 3 ] Apply row transformations R 4 − 2 R 1 → R 4 to reduce it to the row-echelon form as, A = [ 1 1 1 1 0 0 − 2 − 5 − 2 − 1 0 − 3 − 1 3 − 7 0 0 1 2 − 3 ] Apply row transformations 1 − 2 R 2 → R 2 to reduce it to the row-echelon form as, A = [ 1 1 1 1 0 0 1 2

7th Edition

ISBN: 9781305115545

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 6, Problem 11E

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The complete solution of the given system of equations by Gauss Elimination method.

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Chapter 6, Problem 10E

Chapter 6, Problem 12E

Chapter 6 Solutions

College Algebra

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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To find: The complete solution of the given system of equations by Gauss Elimination method.

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Chapter 6 Solutions

To find:

The complete solution of the given system of equations by Gauss Elimination method.