Exercise 1 In this exercise you will be walked through the entire process in the "distinct real roots case". We will find the general solution to the equation: x' = Ax where A = (1) Find the characteristic polynomial p(X) of A, then use this polynomial to determine the eigenvalues of A. (2) In this case there are two eigenvalues , and 12. For each eigenvalue A; find an associated eigenvector vi (each eigenspace will be one dimensional in this case). (3) Write down your general solution: x(t) = Creditvi + Czelatv2. (4) Solve the initial value problem: (i) x' = Ax (ii) x(0) = 1-2