Exercise $3\mathrm{.}3$

a$.$ Enter the above adjacency matrix A into MATLAB. By looking at the entry of $A^3$ in the first

row and the fifth column, find the number of ways to get from San Diego to Manila with

exactly two stops. Include your input and output in your document. Does your answer here

agree with your explicit count in the previous exercise? If not, add the missing trips to your

answers of the previous exercise.

b$.$ Now use MATLAB find the number of ways to get from Manila to Seattle with at most four

stops. Note that this is not the same as finding the number of ways with exactly four stops!

Include all of your commands and output in your write$-$up$.$