What is the augmented matrix of the following system? \[ \begin{array}{r} 3 x+4 y=6 \\ -12 x+16 z=1 \\ -7 y+z=4 \end{array} \]

Step 1 ：The augmented matrix is a matrix that is obtained from a system of linear equations. Each row of the matrix represents a single equation from the system, and each column represents a coefficient of one of the variables. The last column represents the constants on the right side of the equations.

Step 2 ：To form the augmented matrix from the given system of equations, we need to write down the coefficients of each variable in each equation in a row of the matrix. If a variable is missing in an equation, its coefficient is zero.

Step 3 ：The coefficients of the given system of equations are [[3, 4, 0, 6], [-12, 0, 16, 1], [0, -7, 1, 4]].

Step 4 ：Thus, the augmented matrix of the given system of equations is \[\boxed{\begin{array}{cccc}3 & 4 & 0 & 6 \\ -12 & 0 & 16 & 1 \\ 0 & -7 & 1 & 4\end{array}}\]