Solve the system of equations by using the inverse of the coefficient matrix if it exists and by the Gauss-Jordan method if the inverse doesn't exists.
\[
\begin{aligned}
4 x-4 y & =9 \\
20 y+80 z & =128 \\
x+4 z & =8
\end{aligned}
\]
What is the inverse of the coefficient matrix?
A. The inverse matrix is $\square$. (Type a matrix, using an integer or simplified fraction for each matrix element. Do not factor out a scalar multiple.)
B. There is no inverse of the given matrix.

Step 1 ：First, we need to write the system of equations in matrix form. The coefficient matrix is then given by the coefficients of the variables in the system of equations.

Step 2 ：The coefficient matrix A is \[\begin{bmatrix} 4 & -4 & 0 \\ 0 & 20 & 80 \\ 1 & 0 & 4 \end{bmatrix}\]

Step 3 ：We can then calculate the determinant of this matrix. If the determinant of the matrix is not zero, then the inverse exists. If the determinant is zero, then the inverse does not exist.

Step 4 ：The determinant of the coefficient matrix A is approximately zero.

Step 5 ：Since the determinant of the coefficient matrix is approximately zero, this means the inverse of the matrix does not exist.

Step 6 ：Final Answer: \(\boxed{\text{There is no inverse of the given matrix.}}\)