Practice Final Question #1
alexwang0518
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)=( λ-2)$( 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