Answer Happy

Problem 2: Naren is dating a girl named Felicity. Naren and Felicity both cautiously follow their hearts if one has positive feelings towards the other, those positive feelings slowly amplify. However, Naren puts tremendous weight on Felicity's feelings towards him-if
Felicity likes him, he likes her much more, and if Felicity dislikes him, he likes her less. Felicity, on the other hand, does not like "clingy" people--if Naren likes her more, she tends to like him a little bit less. She is also susceptible to playing "hard to get"-if Naren dislikes her, she tends to like him more. Being an engineer, Naren has modeled these emotional dynamics with the following set of coupled ordinary differential equations: N(t) = 0.1N (t) + 1F(t) F(t) = -0.5N (t) + 0.1F(t), Solve the system of o.d.e.s by hand using eigenvalues and eigenvectors to determine the fate of "Naricity" if N(0) = 1 and F(0) = 0, and plot the solution parameterized by t from t = 0 to t = 10, i.e., plot F(t) vs. N(t). What will become of Naricity? You may use MATLAB's left division to solve systems of linear equations. Suggestion: You must show your work, but use MATLAB as your calculator because the numbers are a little annoying.