Final answer:
Elementary row operations on an augmented matrix, which include swapping rows, multiplying a row by a non-zero constant, and adding multiples of one row to another, do not change the solution set of the associated linear system.
Step-by-step explanation:
The question asks whether performing elementary row operations on an augmented matrix changes the solution set of the associated linear system. I'm happy to clarify that elementary row operations do not change the solution set. These operations include swapping rows, multiplying a row by a non-zero constant, and adding a multiple of one row to another row. Their purpose is to simplify the matrix to a form where the solution set can be more easily identified, in what is known as row-echelon form or reduced row-echelon form.
There are techniques to approach solving systems of linear equations, but the fundamental aim of using row operations is to maintain the equivalence of the original system. As long as the operations are applied correctly, the augmented matrix will always represent a linear system that has the same solutions as the one we started with, hence not altering the related equations' consistency and independence.