question below: Can you use the pairing sc-3 a=0, b=3, c= -1, d= 3, x(0)=[4,7]

You are designing an online dating app. Each user has a love profile that governs how they tend to love. For example, Garth's love style is Simple (S). when Garth is in love with someone, he falls more deeply in love the more that person loves him. On the other hand, Hanna has a more Complicated (C) love style. She likes the feeling of being in love, which in turn makes her love grow even more. To temper this, the more her love interest loves her, the less love she is inclined to feel for that person. The following details of this example demonstrate how we can model this situation using a system of linear differential equations. Let G(t) represent Garth's love for Hanna at time t years, and H(t) Hanna's love for Garth at time tyears. The rate of change of Garth's love for Hanna is proportional to her love for him. So we could write that as G'(t) = b H(t), where b>0 is some proportionality constant. The more Hanna loves Garth, the better she feels, inspiring her to love him even more. This means the rate of change of her love for Garth, H'(t), is proportional to her love for Garth, H(t), and d>0will be the proportionality constant for that. The more Garth loves Hanna, though, she is less inclined to love him. And so we're going to have a negative proportionality constant c times G(t), where c0,c>0. SIC-1:a=0,b>0,c0,d2+4bc0,co,d2+4bc=o slc-sza=o,b>o,co,d2+4bc>o C/C1:a>0, b0, adbc0, b0, adbc=0 C/C-3:a>0, b0, ad-bc>0 - Choose values for a, b, c, and d that fit one of the seven love style pairings, and put these, and which love style pairing (e.g. SIC-2) they fit into, along with the name of your dating app, in the subject heading. Your choices of a, b, c, and d cannot be the same as anyone else's. There is also a limit of 5 students per love style pairing. 0 Set the initial love values for your two clients. These values should be in the range [-10,10]. 0 Set up the initial value problem in matrix form. - Solve the initial value problem, showing the details of all of your steps. 0 Use a parametric plotter to plot the clients' love graph with a window of [-500,500]x[-500,500], and t from 0 to 10 years. You don't have to graph any parts that go outside your window. Garth and Hanna's example is graphed below (their love went out of bounds well before the 10 year mark!). Figure: A Parametric Plot of the Solution shows Garth's and Hanna's love for each other spiraling out of control. l 400 t l Figure Generated From: Wolfram Alpha: Computational Knowledge Engine. (2009). Retrieved April 30, 2016, from https://www.wolframalpha.com - Analyze the clients' predicted love path over the next 10 years. If their love goes outside the lower (negative) range in either direction, their relationship is destined to fail. If that occurs, when in their relationship does it occur? 0 Describe the quality of their love relationship in the early stages, mid stages and later stages of their relationship over 10 years. 0 Would you advise this love style pairing to your clients? Why or why not? 0 You must have at least one main post that includes a full mathematical explanation, and at least two other substantive discussion posts to satisfy the requirements for this Exploration Discussion