\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.