To practice the methods of this section, do not use an eigenvector routine from your matrix program. Instead, use the program to find the eigenvalues, and, for each eigenvalue λ, find an orthonormal basis for Nul(A – λI), as in Examples 2 and 3.

Data From Section 7.1 Example 2 and 3

EXAMPLE 2 If possible, diagonalize the matrix A = 6-2 -1 6-1 -2 -1 -1 5