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. O A. 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. O B. 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. O C. The statement is true. Elementary row operations are always applied to an augmented matrix after the solution has been found. O D. The statement is true. Each elementary row operation replaces a system with an equivalent system.
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. O A. 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. O B. 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. O C. The statement is true. Elementary row operations are always applied to an augmented matrix after the solution has been found. O D. The statement is true. Each elementary row operation replaces a system with an equivalent system.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
O A. 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.
O B. 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.
OC. The statement is true. Elementary row operations are always applied to an augmented matrix after the solution has been found.
O D. The statement is true. Each elementary row operation replaces a system with an equivalent system.
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