For the system of linear equations, which of the following is not true?
1) If the system has a unique solution, then the determinant of the coefficient matrix is non-zero.
2) If the system has infinitely many solutions, then the determinant of the coefficient matrix is zero.
3) If the system has no solution, then the determinant of the coefficient matrix is non-zero.
4) If the system has no solution, then the determinant of the coefficient matrix is zero.