Let M be a 2 x 2 matrix with eigenvalues A₁ = 0.3, A2= -0.25 with corresponding eigenvectors = [2²] ²2² = [9] · V₂ Consider the difference equation with initial condition Xo That is, write xo = C1V1 + C₂V2 H Write the initial condition as a linear combination of the eigenvectors of M. In general, x Specifically, X4 V1 = For large k, xk Xk+1 = V₁+ )k v₁+ Mxk T V2

Let M be a 2 × 2 matrix with eigenvalues ₁ = -1.2, A2 = 1 with corresponding eigenvectors Consider the difference equation with initial condition Xo = 5 3 V₁ = V2 = 2 xk+1 = Mxk Write the initial condition as a linear combination of the eigenvectors of M. That is, write x0 = c1V1 + C₂ V₂ = In general, xk= V1+ V2 ) * vi+ k ) v2 Specifically, x4 = For large k, xk≈ k

Consider the matrix 2 -4 A = (-²₁ 2¹) -1 (a) Compute the eigenvalues and the corresponding eigenvectors. (b) Let v = = [2, 1], compute A10¹0000 V.

A H the eigenvalues X₁ = 2 and A₂ = -1, respectively. What is A(v₁ + V₂)? Suppose A is a 3 x 3 matrix with eigenvectors V₁ A 3 2 B Ⓡ = 0 and V₂ = 2 -2 corresponding to D H