Final answer:
The correct answer is that the system cannot have a unique solution when the coefficient matrix is singular. This is because the determinant is zero, making the system either inconsistent or dependent on infinitely many solutions. The correct answer is B.
Step-by-step explanation:
If the coefficient matrix of a system of linear equations is square but not invertible, which implies that it is a singular matrix, one statement about the solution set of the system is true. The correct answer is: b. the system cannot have a unique solution.
When a square matrix is singular, it means its determinant is zero, indicating that the system of equations is either inconsistent (no solution) or has infinitely many solutions (dependent system). A unique solution would only be possible if the matrix were non-singular (invertible).
In other words, for a system of equations, if the coefficient matrix is singular, the system will likely have either no solutions or an infinite number of solutions. This is because the equations are linearly dependent. This precludes the possibility of a unique solution because the determinant of the matrix, which is calculated during the process of finding solutions via methods such as row reduction or matrix inversion, is zero.