Editing Good Will Hunting (section)

===The first blackboard problem===
Near the start of the film, Will sets aside his mop to study a difficult problem posed by Lambeau on the blackboard.<ref>[[Burkard Polster]] & Marty Ross (2012) ''Math goes to the Movies'', [[Johns Hopkins University Press]], page 9, {{ISBN|1-4214-0483-4}}</ref> The problem has to do with intermediate-level [[graph theory]], but Lambeau describes it as an advanced "[[Fourier analysis|Fourier]] system".

To answer the first part of the question, Will chalks up an [[adjacency matrix]]:
:<math>A=\begin{pmatrix} 0 & 1 & 0& 1 \\ 1 & 0 & 2 & 1 \\ 0 & 2 & 0 & 0 \\ 1 & 1 & 0 & 0 \end{pmatrix}.</math> 
To answer the second part, he determines the number of 3-step [[walk (graph theory)|walks]] in the graph, and finds the third power matrix:
:<math>A^3=\begin{pmatrix} 2 & 7 & 2 & 3 \\ 7 & 2 & 12 & 7 \\ 2 & 12 & 0 & 2 \\ 3 & 7 & 2 & 2 \end{pmatrix}.</math>
The third and fourth parts of the question concern [[Generating function#Example: Spanning trees of fans and convolutions of convolutions|generating functions]]. The other characters are astounded that a janitor shows such facility with [[matrix (mathematics)|matrices]].