Just need for someone to help me out with the rest of the pr

Just need for someone to help me out with the rest of the problem. I believe that I got the eigenvalues which are 3+2i and 3-2i but I could be wrong. Thanks!

Entered Answer Preview Result Messages | Eigenvalues-a, 2. c:a, 2), da(-,- Eigenvalues = (3, 2), c = (3,2), d = incorrect You need to enter the eigenvectors The answer above is NOT correct. (1 point) The matrix A-34 has complex eigenvalues, 1,2-a ± bi, where a = | 3 3 -4 10 9 and b =12 The corresponding eigenvectors are v1,2-c ± d, where c = [ and d = [

Solution

|A -Ix| =0

(-3 -x)*(9 -x) +40 =0

-(x+3)(9-x) +40 =0

-( x^2 +9x +27 -3x) +40 =0

-x^2 -6x +13 =0

x = 3 - 2i ; x = 2i +3

Eigen Values are : x= 3 -2i , 2i +3

Eigen Vectors : x = 3- 2i ; c = [ 1, ( i-3)/2 ]

x = 2i +3 ; d= [1 , -(i+3)/2 ]