The matrix M = L - A2 = 0 0 -2 -2 0 -2 -2 0 -2 Find the eigenvalues and an orthonormal basis for each eigenspace. A₁ = -4 0 -2 Orthonormal basis of eigenspace: | has two distinct eigenvalues ₁

Find a 3 x 3 matrix A whose -4-eigenspace is and whose 3-eigenspace is A = V = {(x, y, z) in R³ | -8x14y + 10z = 0} 8pc (C) {}} W = Span

For the matrix A, find (if possible) a nonsingular matrix P such that P-!AP is diagonal. (If not possible, enter IMPOSSIBLE.) 6 -3 A = -2 P = Verify that P-'AP is a diagonal matrix with the eigenvalues on the main diagonal. P-1AP =

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