Explanation Approach: If the system of linear equations is not inconsistent and all the variable in the row-echelon form are not leading variables, then it has infinitely many solutions, and the system is called dependent. If the row echelon form contains a row that represents the equation 0 = c , then the system has no solution. If the system of linear equations has no solutions, then it is inconsistent. Calculation: Consider the system of equations { x + 4 y − 2 z = − 3 2 x − y + 5 z = 12 8 x + 5 y + 11 z = 30 . The augmented matrix is [ 1 4 − 2 − 3 2 − 1 5 12 8 5 11 30 ] . Transform the augmented matrix into row echelon form. Perform the transformation R 2 → R 2 − 2 R 1 . [ 1 4 − 2 − 3 2 − 2 ( 1 ) − 1 − 2 ( 4 ) 5 − 2 ( − 2 ) 12 − 2 ( − 3 ) 8 5 11 30 ] → [ 1 4 − 2 − 3 0 − 9 9 18 8 5 11 30 ] Perform the transformation R 3 → R 3 − 8 R 1 . [ 1 4 − 2 − 3 0 − 9 9 18 8 − 8 ( 1 ) 5 − 8 ( 4 ) 11 − 8 ( − 2 ) 30 − 8 ( − 3 ) ] → [ 1 4 − 2 − 3 0 − 9 9 18 0 − 27 27 54 ] Perform the transformation R 2 → − R 2 9

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 11.1, Problem 45E

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Whether the system of equation {x+4y−2z=−32x−y+5z=128x+5y+11z=30 is inconsistent or dependent. If dependent, write the complete solution.

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Chapter 11.1, Problem 44E

Chapter 11.1, Problem 46E

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Chapter 11 Solutions

Algebra and Trigonometry (MindTap Course List)

Ch. 11.1 - If a system of linear equations has infinitely...Ch. 11.1 - Write the augmented matrix of the following system...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - 5-10 Dimension of a Matrix State the dimension of...Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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Whether the system of equation { x + 4 y − 2 z = − 3 2 x − y + 5 z = 12 8 x + 5 y + 11 z = 30 is inconsistent or dependent. If dependent, write the complete solution.

Solution Summary: The author analyzes whether the system of equations cx+4y-2z=-3 2x-y+5z = 12 8x +5y +11z

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Whether the system of equation {x+4y−2z=−32x−y+5z=128x+5y+11z=30 is inconsistent or dependent. If dependent, write the complete solution.

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Chapter 11 Solutions