Calculate \\( M_X^4 * M_\Phi * M_Y^3 \\), remembering to do matrix multiplication
according to the (min, +)-formula for matrix multiplication in the quantale **Cost**;
see [Eq. (2.97)](https://forum.azimuthproject.org/discussion/2118).

Your answer should agree with what you got in [Exercise 4.15](https://forum.azimuthproject.org/discussion/2234); does it?

[Previous](https://forum.azimuthproject.org/discussion/2234)
[Next](https://forum.azimuthproject.org/discussion/2243)


\[
\begin{matrix}
\begin{array}{c | c c c c}
M_X & A & B & C & D \\\\
\hline
A & 0 & \infty & 3 & \infty \\\\
B & 2 & 0 & \infty & 5 \\\\
C & \infty & 3 & 0 & \infty \\\\
D & \infty & \infty & 4 & 0
\end{array}
&
\begin{array}{c | c c c c}
M_{\Phi} & x & y & z \\\\
\hline
A & \infty & \infty & \infty \\\\
B & 11 & \infty & \infty \\\\
C & \infty & \infty & \infty \\\\
D & \infty & 9 & \infty
\end{array}
&
\begin{array}{c | c c c c}
M_Y & x & y & z \\\\
\hline
x & 0 & 4 & 3 \\\\
y & 3 & 0 & \infty \\\\
z & \infty & 4 & 0
\end{array}
\end{matrix}
\]