# Question 5 Suppose that A is the matrix (51 -1 A= 0 4 0 1 1...

###### Question:

Question 5 Suppose that A is the matrix (51 -1 A= 0 4 0 1 1 3 (a) Find an invertible matrix P such that P-1AP = J where J is a Jordan normal form. Now consider the system of differential equations f'(t) = 5f(t) +g(t) - h(t), 9'(t) = 49(t) and h'(t) = f(t)+g(t) + 3h(t). (b) Find the general solution to this system of differential equations. (c) What is the dominant long-term behaviour of this system? For what initial conditions will this long-term behaviour not occur? (d) Find the particular solution when f(0) = 1,90) = 0 and h(0) = 0.

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