Let x, y be nonzero vectors in Rn, n ≥ 2, and letA = xyT . Show that λ = 0 is an eigenvalue of A with n − 1 linearly independent eigenvectors and consequently has multiplicity at least n − 1

Let be an eigenvector of a matrix A corresponding to the eigenvalue 1, = -1 and the vector be an eigenvector of A corresponding to the eigenvalue 1, = 4. Which of the following is equal to A. e) L d-) e-) nndiğini görene kadar hekleviniz Soruvu bos birakmak isterseniz işarett

Let M be a 2 × 2 matrix with eigenvalues ₁ = -0.8, 12 = 1 with corresponding eigenvectors Consider the difference equation with initial condition X = V₁ = V2 = Xk+1 = Mxk Write the initial condition as a linear combination of the eigenvectors of M. That is, write x0 = c1V1 + C2V2 = In general, X = Vi+ V2 k )* VI+ ) k V2 Specifically, X2 = For large k, xk →

(3) Let matrix A have eigenvectors . . associated with eigenvalues Xo = 4, A₁ = 2, A₂ = 0), respectively. Suppose some vector 7 is: 7 = №n +27₁ +30¹₂ Compute Ar. Give your result as a linear combination of eigenvectors ₁.