Hello. Please answer the following question, ensure that your answer is correct and supported by calculations, explanations and algebraic work. Only utilize the sections/topics seen below. Solutions for Ordinary Differential Equations must be given in real values form(i.e. no complex or imaginary values). Please organize your work, in a reasonably neat and coherent way. Do not use ChatGPT, I will not be able to rate you highly if this is not your work. Thank you so much, I hope you have a great day!

Topics: first order linear (autonomous) systems linear systems II (like phase planes and direction fields) linear systems III(like eigenvalues and eigenvectors) linear systems IV (like rewriting undamped oscillators as a system, using eyelets principle and linearity principle, classification of equilibrium point Linear systems V (eigenvalues, trace of a matrix) Systems (evecs)

For the equations below: ' =3zvy, Y =z4+9 a) write an equivalent first order system. b) determine the dimension of the system. c) State whether or not it is linear, and if linear, state whether or not it is homogeneous. d) If the system is linear, rewrite in matrix form