Which of the following best describes a coefficient matrix?

The description of a coefficient matrix focuses on its role in representing the numerical factors associated with the variables in a system of linear equations. A coefficient matrix is constructed by taking the coefficients that are multiplied by each variable in the equations and arranging them into a matrix format. This structure allows for efficient manipulation and solution of the system using linear algebra techniques.

For example, in a system of equations like:

1. 2x + 3y = 5
2. 4x - y = 2

The coefficient matrix would include the coefficients 2 and 3 from the first equation, as well as 4 and -1 from the second equation, resulting in:

[ \begin{bmatrix} 2 & 3 \ 4 & -1 \end{bmatrix} ]

This matrix provides a clear representation of the relationships between the variables and the equations, enabling the use of methods such as row reduction or matrix operations to find solutions efficiently.

While other options mention various types of matrices, they do not accurately capture the specific function of a coefficient matrix within the context of linear systems. For example, a matrix containing variables or one representing output values does not convey the necessary information to describe the coefficients explicitly, and a transformation