The matrix A = The larger eigenvalue 2₂ is -1 7 4 1 3 -1 5 -3 -1 2 -3 1 1 6 -4 has two distinct real eigenvalues λ₁ <^₂. Find the eigenvalues and a basis for each eigenspace. The smaller eigenvalue ₁ is. and a basis for its associated eigenspace is (-) and a basis for its associated eigenspace is (EE))

The matrix The eigenvalue 1 is 0 A = 1 1 0 1 -1 has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace. The eigenvalue λ2 is -1 1 2 and a basis for its associated eigenspace is { and a basis for its associated eigenspace is

A diagonalization of the matrix A is given in the form P-¹AP = D. List the eigenvalues of A and bases for the corresponding eigenspaces. (Repeated eigenvalues should be entered repeatedly with the same eigenspaces.) d₁= = ^₂ = 13 = 1007240 18 1007/N +10 18 18 2 1 4 1 2 5 9 4 4 4 0 0 1 4 4 3 9 1 0 1 -1 1 8 0 -1 has eigenspace span has eigenspace span has eigenspace = 80 0 00 0 0 0 -1 (LF) span (smallest λ-value) (largest λ-value)

The matrix * 8 0. A = 0. -2 -2 -6 has one real eigenvalue. Find this eigenvalue and a basis of the eigenspace. The eigenvalue is A basis for the eigenspace is