Chapter 5.3, Problem 17E

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).

17. $\left[\begin{array}{ccc}4& 0& 0\\ 1& 4& 0\\ 0& 0& 5\end{array}\right]$