154 CHAPTER 6. SPECTRAL THEORY

8. Find the eigenvalues and eigenvectors of the matrix

 −3 −7 19

−2 −1 8

−2 −3 10

 .Determine

whether the matrix is defective.

9. Find the eigenvalues and eigenvectors of the matrix

 −7 −12 30

−3 −7 15

−3 −6 14

 .

10. Find the eigenvalues and eigenvectors of the matrix

 7 −2 0

8 −1 0

−2 4 6

 . Determine

whether the matrix is defective.

11. Find the eigenvalues and eigenvectors of the matrix

 3 −2 −1

0 5 1

0 2 4

 .

12. Find the eigenvalues and eigenvectors of the matrix

 6 8 −23

4 5 −16

3 4 −12

. Determine

whether the matrix is defective.

13. Find the eigenvalues and eigenvectors of the matrix

 5 2 −5

12 3 −10

12 4 −11

 . Determine

whether the matrix is defective.

14. Find the eigenvalues and eigenvectors of the matrix

 20 9 −18

6 5 −6

30 14 −27

 . Determine

whether the matrix is defective.

15. Find the eigenvalues and eigenvectors of the matrix

 1 26 −17

4 −4 4

−9 −18 9

 . Determine

whether the matrix is defective.

16. Find the eigenvalues and eigenvectors of the matrix

 3 −1 −2

11 3 −9

8 0 −6

 . Determine

whether the matrix is defective.

17. Find the eigenvalues and eigenvectors of the matrix

 −2 1 2

−11 −2 9

−8 0 7

 . Determine

whether the matrix is defective.