Eigen vectors of are

To find the eigenvectors of a matrix, we solve the equation (A - λI)v = 0 for each eigenvalue λ. For a matrix with entries like [1 cos; cos 1], the characteristic equation yields eigenvalues λ = 1 + cos and λ = 1 - cos. Substituting these back into the equation gives us the corresponding eigenvectors. For λ = 1 + cos, we get v₁ = [1; -1]. For λ = 1 - cos, we get v₂ = [1; 1]. Option B correctly identifies these eigenvector forms. Other options like A, C, and D either represent incorrect eigenvalues or unrelated matrix operations (like powers of matrices). Thus, Option B is the correct choice.