Diagonalize the matrices in Exercises 7-20, if possible. The eigenvalues for Exercises 11-16 are as follows: (11) λ = 1, 2, 3; (12) λ = 2,8; (13) λ = 5, 1; (14) λ = 5,4; (15) λ = 3,1; (16) λ = 2, 1. For Exercise 18, one eigenvalue is λ = 5 and one eigenvector is (-2, 1, 2).
7.1 0 8. 5 1 9. 3 -1
6 -1 0 5 1 5
10. 2 3 11. -1 4 -2 12. 4 2 2
4 1 -3 4 0 2 4 2
-3 1 3 2 2 4
13.2 2 -1 14. 4 0 -2 15. 7 4 16
1 3 -1 2 5 4 2 5 8
-1 -2 2 0 0 5 -2 -2 -5