\begin{equation*} \left [ \begin{array}{ccccc|c} \blacksquare & \ast & \ast & \ast & \ast & \ast \\ 0 & \blacksquare & \ast & \ast & \ast & \ast \\ 0 & 0 & \blacksquare & \blacksquare & \ast & \ast \\ 0 & 0 & 0 & 0 & \blacksquare & 0 \end{array} \right ] \end{equation*}
Which of the following is true? Select all that apply.
The corresponding system of equations is consistent. The corresponding system of equations is inconsistent. The rank
of the augmented matrix is \(4\). The rank of the augmented matrix is \(5\). The rank of the augmented matrix is \(6\). There are no
free variables. There is one free variable. There are two free variables. The corresponding system has a unique solution.
The corresponding system has infinitely many solutions.