12.5. EXERCISES 281

14. Find the eigenvalues and eigenvectors of the matrix 3 −2 −10 5 10 2 4

 .

Determine whether the matrix is defective.

15. Find the eigenvalues and eigenvectors of the matrix 6 8 −234 5 −163 4 −12

Determine whether the matrix is defective.

16. Find the eigenvalues and eigenvectors of the matrix 5 2 −512 3 −1012 4 −11

 .

Determine whether the matrix is defective.

17. Find the eigenvalues and eigenvectors of the matrix 20 9 −186 5 −6

30 14 −27

 .

Determine whether the matrix is defective.

18. Find the eigenvalues and eigenvectors of the matrix 1 26 −174 −4 4−9 −18 9

 .

Determine whether the matrix is defective.

19. Find the eigenvalues and eigenvectors of the matrix 3 −1 −211 3 −98 0 −6

 .

Determine whether the matrix is defective.