Final answer:
The question focuses on performing an elementary row operation on a matrix, which is a topic in linear algebra, relevant to high school and early college mathematics.
Step-by-step explanation:
The question involves Siobhan performing an elementary row operation on a matrix A. In matrix notation, this elementary row operation is represented by 2R3−R2, which refers to multiplying the third row (R3) of the matrix by 2 and then subtracting the second row (R2) from the result. This operation is part of the process of performing Gaussian elimination or row reduction to solve systems of linear equations or to find the inverse of a matrix.
The concept of adding and subtracting rows is analogous to determining the resultant vector R, which can be computed by adding vector components of vectors A and B as per the provided equations. For example, the resultant vector R in its component form is RxÎ + RyĴ + Rz where each component Rx, Ry, and Rz is the sum of corresponding scalar components of vectors A and B, which follows the principle of vector addition in physics.
Understanding how to perform and apply these row operations is fundamental in linear algebra, which is a key component of higher-level mathematics often encountered in college courses but introduced in advanced high school classes.