Question: How do you determine the matrix A for my network of pages using Linear Algebra (Google's PageRank algorithm)?

Think of ranking as a vector in R^Z, where Z is the total number of webpages on the web.

For a given network of Z web pages, let A = [a_jk(little)] be the matrix

a_jk(little) = { 1 if page k has a link to page j

                  { 0 otherwise

1. How do you determine the matrix A for my network of pages?

2. And the number of recommendations that page j gets is v_j = a_j1 + a_j2 + ... + a_iZ, and define this number as the ranking of webpage j. You can determine the ranking as a vector v E(curvy) R^Z, as a matrix vector product, using the matrix A. Now based on those info, how do you determine the vector u, which gives the ranking?

I've been trying to learn Google PageRank algorithm with linear algebra, and I couldn't quite solve these problems. Please try to show steps and explanations as I am trying to learn.