5. [1+1+2pt] The Google page rank algorithm has a lot to do with the eigenvector corre- sponding to the largest eigenvalue of a so-called stochastic matrix, which describes the links between websites. Stochastic matrices have non-negative entries and each column sums to 1, and one can show (under a few technical assumptions) that it has the eigenvalues A1 1 IA2I 2... 2 An Thus, we can use the power method3 to find the eigenvector v corresponding to A1, which can be shown to have either all negative or all positive entries. These entries can be interpreted as the importance of individual websites Let us construct a large stochastic matrices (pick a size n 100, the size of our "toy internet") in MATLAB as follows: A (max (2 randn (n ,n) )-2) A A diag (diag (A)) L A diag (1./(max(1e-10, sum (A, 1))))