Using power method to calculate dominant eigenvalue and eigenvectors

[savva]

Homework Statement

Use the power method to calculate the dominant eigenvalue and its corresponding eigenvectors for the matrices.
The questions are attached with this thread. I have attempted both and seem to have done the first question correctly. I am attempting the second question and am stuck as after finding one eigenvector I got the same result again. Can anybody help me out with what I have to do here?

Also, when taking out a value from the matrix, should it be the middle value or the highest value in the matrix?

Homework Equations

The Attempt at a Solution

 

[Joffan]

Sounds like you found an eigenvector with eigenvalue 1, congratulations :-)

But you should probably try another, orthogonal, start vector too to see if there's another larger eigenvalue.