282 CHAPTER 12. SPECTRAL THEORY

20. Find the eigenvalues and eigenvectors of the matrix −2 1 2−11 −2 9−8 0 7

 .

Determine whether the matrix is defective.

21. Find the eigenvalues and eigenvectors of the matrix 2 1 −12 3 −22 2 −1

 .

Determine whether the matrix is defective.

22. Find the complex eigenvalues and eigenvectors of the matrix 4 −2 −20 2 −22 0 2

 .

23. Find the eigenvalues and eigenvectors of the matrix 9 6 −30 6 0−3 −6 9

 .

Determine whether the matrix is defective.

24. Find the complex eigenvalues and eigenvectors of the matrix 4 −2 −20 2 −22 0 2

 .

Determine whether the matrix is defective.

25. Find the complex eigenvalues and eigenvectors of the matrix −4 2 02 −4 0−2 2 −2

 .

Determine whether the matrix is defective.

26. Find the complex eigenvalues and eigenvectors of the matrix 1 1 −67 −5 −6−1 7 2

 .

Determine whether the matrix is defective.