For the following questions, please clearly write your solutions on a separate piece of paper and upload a pdf of your solutions to this question. 1. A planar system has eigenvalues A = 3 (with...

Extracted text: For the following questions, please clearly write your solutions on a separate piece of paper and upload a pdf of your solutions to this question. 1. A planar system has eigenvalues A = 3 (with associated eigenvector v,) and A, =-1 (with associated eigenvector v,). The eigenvectors are shown below. Copy the eigenvectors to a graph on your paper, and sketch the behavior of a solution with initial value in each of the identified regions 1 through 6. 4. 12 3 96. You must show 2. Find the general solution to the system y' = Ay when A = all steps in arriving at your final answer! 3 Consider the non-linear system y = Y1 (2 – 32). 2 = Y½ (Yn – 3) A. Verify that both (0, 0) and (3, 2) are equilibrium points of this system. B. Compute the linearization of this system at (0,0). You need not make any interpretation using the linearization -- just compute it C. Compute the linearization of this system at (3, 2). You need not make any interpretation using the linearization -- just compute it. Upload Choose a File