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ermine whether the statement below is true or false. Justify the answer. Elementary row operations on an augmented matrix never change the solution set of the associated linear system. pose the correct answer below. A. The statement is true. Each elementary row operation replaces a system with an equivalent system. B. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, scaling a row by a nonzero constant can change the solution set of that system. C. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, replacing one row by the sum itself and a multiple of another row can change the solution set of that system. D. The statement is true. Elementary row operations are always applied to an augmented matrix after the solution has been found.

ermine whether the statement below is true or false. Justify the answer. Elementary row operations on an augmented matrix never change the solution set of the associated linear system. pose the correct answer below. A. The statement is true. Each elementary row operation replaces a system with an equivalent system. B. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, scaling a row by a nonzero constant can change the solution set of that system. C. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, replacing one row by the sum itself and a multiple of another row can change the solution set of that system. D. The statement is true. Elementary row operations are always applied to an augmented matrix after the solution has been found.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.1: The Graphing Method
Problem 3CE
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Determine whether the statement below is true or false. Justify the answer Elementary row operations on an augmented matrix never change the solution set of the associated linear system. Choose the correct answer below. • A. The statement is true. Each elementary row operation replaces a system with an equivalent system. • B. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, scaling a row by a nonzero constant can change the solution set of that system. • C. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, replacing one row by the sum of itself and a multiple of another row can change the solution set of that system. D. The statement is true. Elementary row operations are always applied to an augmented matrix after the solution has been found.
Transcribed Image Text:Determine whether the statement below is true or false. Justify the answer Elementary row operations on an augmented matrix never change the solution set of the associated linear system. Choose the correct answer below. • A. The statement is true. Each elementary row operation replaces a system with an equivalent system. • B. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, scaling a row by a nonzero constant can change the solution set of that system. • C. The statement is false. Interchanging two rows never changes the solution set of the associated linear system. However, replacing one row by the sum of itself and a multiple of another row can change the solution set of that system. D. The statement is true. Elementary row operations are always applied to an augmented matrix after the solution has been found.
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