Where are you stuck? What have you tried? It will be easier to help you if you tell us
(Where A is 3 x 3 matrix ) If A =[1 0 0
0 2a b
0 b 2c]
show that A has only real eigenvalues by finding explicitly the solutions of the characteristic equation.
find the eigenvectors when
i) a is not equal c and b is not equal 0
ii)a=c and b is not equal to 0
iii)a=c and b=0
Can you show as much working as possible
Im stuck when evaluating the determinant as the values of a and c are still involved