Let A= A) This matrix has a repeated eigenvalue. Find it, the cor- responding eigenvector, and the generalized eigenvector. B) Find the solution of the IVP X'(t) = AX(t) with 7(0) = Combine like terms so that the solution has the form vjeat + [13] tv₂eat

The matrix A := C = 12 -2 -3 13 has an eigenvector 6 (8) with eigenvalue 10. What is c?

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

- (1-3). Determine the eigenvalue and corres- 3. a) Given the matrix A = ponding eigenvector and generalized eigenvector of A. b) Determine the general solution of the system of linear differential equations: x₁ = I₁=I₂ x₂ = x1₁+3x₂