Final answer:
The coefficient matrix for the system of equations given (5x - 15y = 15 and -x + 5y = 5) is [[5, -15], [-1, 5]].
Step-by-step explanation:
The coefficient matrix of a system of linear equations is composed of the coefficients of the variables in each equation, organized in rows and columns. For the system of linear equations provided:
5x - 15y = 15
-x + 5y = 5
The coefficient matrix would be:
[[5, -15],
[-1, 5]]
This matrix is created by simply taking the coefficients of x and y from each equation and forming rows in the same order as they appear in the equations.