3. Consider the matrix P = (a) Verify that i is an eigenvector of P and identify the corresponding eigenvalue. (b) Find an eigenvalue that corresonds to = -1.

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

Q1. Find, for the matrix B, the eigenvalues and their corresponding eigenvectors B =[-₂ -¹3]