This is an example of the "double real root easy case".

x' = Ax where A NO C (1) Find the characteristic polynomial p(A) of A, then use this polynomial to determine the eigenvalues of A. (2) In this case, An = > is an eigenvalue of multiplicity two. Since this is the easy case, there will be two linearly independent eigenvectors associated to A := 1 = A2. Find them. (3) Write down the general solution x(t; CI,C2) = Cie*vi + Czekv2 where V1, Va are two linearly independent eigenvectors found in part (3). (4) Solve the initial value problem: (i) x' = Ax (ii) x(0) =