We can create the matrix $A$ as follows:

Suppose we have a set of 3 web pages with the following hyperlink structure:

$v_k = \begin{bmatrix} 1/4 \ 1/2 \ 1/4 \end{bmatrix}$

$v_1 = A v_0 = \begin{bmatrix} 1/6 \ 1/2 \ 1/3 \end{bmatrix}$