re the eigenvectors of A corresponding to the eigenvalue λ = −1 orthogonalwith respect to the usual dot product? If not, apply the Gram-Schmidtprocess to turn them into an orthonormal set of eigenvectors

Are the eigenvectors of A corresponding to the eigenvalue λ = −1 orthogonal with respect to the usual dot product? If not, apply the Gram-Schmidt process to turn them into an orthonormal set of eigenvectors. A=[3,2,4 2,0,2 4,2,3]

Are the eigenvectors of A corresponding to the eigenvalue λ = −1 orthogonal with respect to the usual dot product

Let A=【3 2 4 2 0 2 4 2 3】 You are given that the characteristic equation of A is (λ + 1)2(λ − 8) = 0, i.e. the eigenvalues of A are λ = −1, 8. Are the eigenvectors of A corresponding to the eigenvalue λ = −1 orthogonal with respect to the usual dot product? If not, apply the Gram-Schmidt process to turn them into an orthonormal set of eigenvectors

why can use this step:We can find the eigenvector corresponding to λ1 = 2 by taking the cross product of v2 and v3, since the cross product of two vectors gives a vector that is orthogonal to both. v1 = v2 x v3 = (1,0,1) x (1,2,-1) = (-2, 0, -2

Let A be a 3 × 3 real symmetric matrix and have eigenvalues λ1 = 2, λ2 = λ3 = 1. The eigenvectors corresponding to λ2 = λ3 = 1 are respectively given by v2=(1,0,1), v3=(1,2.-1),Find the eigenvector of A corresponding to λ1 = 2 and the matrix A