Calculating eigenvalues and eigenvectors

[James2012]

Homework Statement

I'm having a problem with a question. I need to find the transition matrix in the form
T=UAU^-1
where U=[V1 V2]

Homework Equations

T=UAU^-1
where U=[V1 V2]

The Attempt at a Solution

my original transition matrix is [0.9 0.002; 0.1 0.998]
from that i calculated the eigenvalues to be 0.898 and 1
which means A=[0.898 0;0 1]
i found the eigenvectors to be V1=[1;-1] and V2=[0.002;0.1]
subbing these into the equation above i end up with the original transition matrix, however the question says to make use of the result [0.02 0.707;0.9998 -0.707]^-1 = [0.9823 0.9823;1.3866 -0.0278]


which means they use different eigenvectors, but I am not sure how they got that

 

[dikmikkel]

I also get the same eigenvals as you but the same vectos as them.

 

[James2012]

Hi, How did you get to the eigenvectors?
i used the equation (A-lamdaI)v=0

then for 0.898 i get the follwing

[0.002 0.002;0.1 0.1][V1;V2]=[0;0]
therefore the eigenvector for 0.898 is [1;-1]