Find the eigenvalues and a set of eigenvectors of the matrix 1 3.1 3 4-2 12 2 Verify that its eigenvectors are mutually orthogonal.

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

Let x = Express as a linear combination of 71, 72, and 73, and find Az. Az = -0--0-0 -1,72 = 3 be eigenvectors of the matrix A which correspond to the eigenvalues ₁-3, A₂ = -2, and A3 = 0, respectively, and let v₁+ V1 = √2+ ~2000 7 x = -5 -8 V3. = 4 2

Show that the eigenvalues of a diagonal matrix are its diagonal elements.