Given the augmented matrix below, determine if the associated system of equations is independent, dependent, or inconsistent.
$$\left[\begin{array}{ccc} -6 &1 &-6\cr 24 &-23 &6\cr -5 &4 &-2 \end{array}\right| \left.\begin{array}{c} 2\cr 1\cr 4 \end{array}\right]$$

The system is ?? independent dependent inconsistent .