1. Consider the differential equation 0 0 15 - Ar,A-1 0 -17 dt for R-R3. (a) Construct a real matrix P such that the change of coordinates Py transforms the original equation to 3 0 0 B=10 2-1 = By, dt [10 marks (b) Solve the system derived in part (a) explicitly for y, and hence evaluate the solution in terms of the original x-coordinates by Py 7 marks (c) Using your solution from part (b), plot trajectories for the particular solution passing through x = [a-b,c,0]T at t = 0, for t E [0,2], where the values of a, b, c are given by the last 3 digits of your student number. This can be done using your favourite mathematical software, e.g. MATLAB 8 marks Act 1. Consider the differential equation 0 0 15 - Ar,A-1 0 -17 dt for R-R3. (a) Construct a real matrix P such that the change of coordinates Py transforms the original equation to 3 0 0 B=10 2-1 = By, dt [10 marks (b) Solve the system derived in part (a) explicitly for y, and hence evaluate the solution in terms of the original x-coordinates by Py 7 marks (c) Using your solution from part (b), plot trajectories for the particular solution passing through x = [a-b,c,0]T at t = 0, for t E [0,2], where the values of a, b, c are given by the last 3 digits of your student number. This can be done using your favourite mathematical software, e.g. MATLAB 8 marks Act