7. (16 pts.) Consider the linear system Y' = AY with A = Y. (a) (12 pts.) Compute the fundamental matrix Yf(t) for this linear system. (b) (4 pts.) Here is a useful fact: eAt = Y,(t)Yf (0)-1. Use this fact to compute eat and solve the IVP Y' = AY with Y (0) = OT CO 1 (c) (Bonus) (2 pts.) Prove the above fact using the uniqueness theorem for linear systems