Consider the initial value problem dx 6 2 dt 20 6 X, X(0) = (a) Find the eigenvalues and eigenvectors for the coefficient matrix. X1 = A, v1 = , and 12 = , U2 = (b) Solve the initial value problem. Give your solution in real form. x (t) = Determine the shape and orientation of solution curves algebraically. An ellipse with counterclockwise orientation 1. Describe the trajectory