Solve the following system by the inverse matrix method, if possible. If the inverse matrix method doesn't apply, use any other method to determine if the system is inconsistent or dependent. If there is a solution, write your answer in the format $(x, y, z)$.
\[
\left\{\begin{aligned}
-4 x+4 y+2 z & =16 \\
x+5 y-z & =19 \\
5 x+y-3 z & =3
\end{aligned}\right.
\]

Step 1 ：Represent the system of equations as a matrix equation of the form AX = B, where A is the matrix of coefficients, X is the column matrix of variables, and B is the column matrix of constants.

Step 2 ：Matrix A is \[\begin{bmatrix} -4 & 4 & 2 \\ 1 & 5 & -1 \\ 5 & 1 & -3 \end{bmatrix}\] and matrix B is \[\begin{bmatrix} 16 \\ 19 \\ 3 \end{bmatrix}\].

Step 3 ：Use the inverse matrix method to solve for X. This involves finding the inverse of A, if it exists, and then multiplying both sides of the equation by A inverse.

Step 4 ：If the inverse of A does not exist, the system is either inconsistent or dependent.

Step 5 ：After calculation, we find that X is \[\begin{bmatrix} -0.5 \\ 4.5625 \\ 0 \end{bmatrix}\].

Step 6 ：Thus, the solution to the system of equations is \(\boxed{(-0.5, 4.5625, 0)}\).