Final answer:
The question involves performing row operations on an augmented matrix in linear algebra, a procedure used in solving systems of equations and in other applications like finding the inverse of a matrix.
The correct option is A.
Step-by-step explanation:
The question asks about performing row operations on an augmented matrix. This is a common procedure in linear algebra, often used in solving systems of equations or finding the inverse of a matrix.
The augmented matrix can be manipulated using various row operations such as swapping rows (denoted by Ri ↔ Rj), multiplying a row by a nonzero scalar (denoted by kRi), and adding a multiple of one row to another row (denoted by Ri + kRj).
Here are the basic steps to perform row operations:
Select the row operation you need to use based on the goal (e.g., making the leading entry of a row 1).
Apply the operation to the augmented matrix, being careful to perform the same operation across the entire row.
Repeat this process as necessary until the augmented matrix is in the desired form, such as reduced row-echelon form (RREF).
It's important to note that row operations do not affect the solutions of the system represented by the augmented matrix. Instead, they simplify the matrix to make it easier to identify the solutions.
The correct option is A.