Formulate the matrix A λI to solve for the eigenvalues. The eigenvalues are λ=2, and λ=1 with an algebraic multiplicity of 2 since you find that the det(A λI)=( λ2)$( λ+1)^{2} .
These eigenvalues placed along the diagonal is the matrix D.
D=
2 0 0
0 1 0
0 0 1
Find eigenvectors for each corresponding eigenvalue by plugging in each corresponding eigenvalue into A λI and row reducing that matrix in order to find the eigenvectors. For λ=2, the eigenvector is (1 1 1 ) (In a column). For λ=1, you get the eigenvectors (1 1 0), (1 0 1).
So Q =
1 1 1
1 1 0
1 0 1
