I was reading my lecture notes on using matrices to solve ODEs and came across this and am having trouble understanding it:
(Please note that the two eigen values that are calculated are 2 and 0 respectively).
I have tried checking the solution and all I am coming up with is a=b (I did this by solving simultaneously. a+b=2a and a+b=2b. I don't understand how the solution v=(1,1)^T comes from. In addition I also do not understand where the solution for the second eigenvalue (0) comes from either.
Please could some one kindly help me understand this. Thank You