x' = (5+3)x + (5-3)y y' = 5x+5y such that P(0) = (x(0), y(0) = (7,0) Solve this linear autonomous DES. then x(0.5). So this question you must: 1. Find the matrix A of the linear autonomous DES (such that P' = AP). 2. Compute the characteristic polynomial of A, pA(x). 3. Find the eigenvalues of A (two distinct real eigenvalues), ^1 and 12. 4. Find the associated eigenspaces, Ex1 and Ex2. 5. Choose an eigenvector for each eigenvalue, v1 and v2: 6. Use the initial condition P(0) = (7, 0), to calculate the coefficients c1 and c2 of the solution: . 7 Evaluate the function x(t) at time t = 0.5.