(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