# Write the transition matrix

1. Dec 19, 2008

### jkeatin

1. The problem statement, all variables and given/known data
p1 goes to p2
p2 goes to p3
p3 goes to p1
p4 goes to p3

Assume that surfers have an 80% chance of following one of the links on the page, and a
20% chance of jumping to a random page.
(a) Write the transition matrix A representing the surfing process.
(b) Is A singular or nonsingular?

2. Relevant equations

3. The attempt at a solution

i got this matrix

.2 .2 (.2*.8) .2
(.2*.8) .2 .2 .2
.2 (.2*.8) .2 (.2*.8)
.2 .2 .2 .2

then do i just let lamda = 1 and find the eigenvector?

2. Dec 19, 2008

### Avodyne

Each column should sum to 1, since that's the total probability. They don't, so you need to think more carefully about what the probabilies are for each transition.

3. Dec 19, 2008

### jkeatin

do i divide every entry in the matrix by 1/4th ?

4. Dec 19, 2008

### jkeatin

.2 1/4th
.2 1/4th *.8
1/4th
1/4th

is that correct for column a?