Consider the following matrix A=[−76−98] a) Find the characteristics equation of A in terms of λ (which can be typed as lambda). b) Determine the eigenvalues of A and their corresponding eigenvectors. Let λ1 and λ2 be the eigenvalues of A such that λ2>λ1, and v1 and v2 their eigenvectors respectively. So, For λ1= , we have v1= For λ2= , we have v2=

a) Find the eigenvalues and the associated eigenvectors of the matrixA = [7 0 −3−9 −2 318 0 −8]

Consider the following matrix.A = 23 12 −36 −19Find the eigenvalues and associated eigenvectors of A. (Arrange the eigenvalues so that 𝜆1 < 𝜆2.)𝜆1 =        with eigenvector    x1 = 𝜆2 =        with eigenvector    x2 =

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. ind an orthogonal matrix P that orthogonally diagonalizes A

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

For each of the following matrices, and eigenvalue λ has been given.[ 0 4−1 5], λ = 4(a)[2 22 −1], λ = −2(b)3 1 −10 1 24 2 0, λ = 3(c)Find one eigenvector corresponding to the given eigenvalue