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## Comments

$$ \begin{array}{ c | c c c c } \nearrow & A & B & C & D \\ \hline A & 0 & \infty & 3 & \infty \\ B & 2 & 0 & \infty & 5 \\ C & \infty & 3 & 0 & \infty \\ D & \infty & \infty & 6 & 0 \end{array} $$

`\[ \begin{array}{ c | c c c c } \nearrow & A & B & C & D \\\\ \hline A & 0 & \infty & 3 & \infty \\\\ B & 2 & 0 & \infty & 5 \\\\ C & \infty & 3 & 0 & \infty \\\\ D & \infty & \infty & 6 & 0 \end{array} \]`

@Bruno You filled out the matrix with paths of length 1 (which is correct). What Happens when you multiply it by itself?

`@Bruno You filled out the matrix with paths of length 1 (which is correct). What Happens when you multiply it by itself?`

@Fredrick, multiplying the matrix by itself (using the Eq. 2.97 that tells us about matrix multiplication in a quantale) yields a matrix that tells us about paths with up to 2 edge-traversals.

`@Fredrick, multiplying the matrix by itself (using the Eq. 2.97 that tells us about matrix multiplication in a quantale) yields a matrix that tells us about paths with up to 2 edge-traversals.`