Given the solution matrix on the calculator with columns x, y, and z, cnoose the correct solution \[ \left[\begin{array}{lll|l} 2 & 0 & 4 & 5 \\ 0 & 3 & 2 & 7 \end{array}\right] \] $(z+5, z+7, z)$ $(-2 z+5 / 2,-2 z / 3+7 / 3, z)$ $(-4 z+5,-2 z+7, z)$ None of these

Step 1 ：The given matrix is in the form of an augmented matrix for a system of linear equations. The first row represents the equation \(2x + 4z = 5\) and the second row represents the equation \(3y + 2z = 7\).

Step 2 ：We can solve this system of equations for x, y, and z. The solutions will be in the form of \(x = ...\), \(y = ...\), \(z = ...\).

Step 3 ：Solving the equations, we get \(x = \frac{5}{2} - 2z\), \(y = \frac{7}{3} - \frac{2z}{3}\), and \(z = z\).

Step 4 ：Comparing these solutions with the given options, it matches with the second option \((-2z + \frac{5}{2}, -\frac{2z}{3} + \frac{7}{3}, z)\).

Step 5 ：Therefore, the correct solution is \(\boxed{(-2z + \frac{5}{2}, -\frac{2z}{3} + \frac{7}{3}, z)}\).