2.- a) find eigenvalue/eigenvalues and the corresponding eigenvector/eigenvectors of A. b) consider the system: (1) A i) if y = 0 then -t Show that the following vector function () = (a+bt) e- is a solution of (1) if and only if c+dt. = (2)) = - (²2) c) use the above exercises to find the general solution d) Asses whether the solution you got consist of two linearly independent functions. e) explain why the solution curves, when t → +∞o are parallel with x-axis f) find the solution curve through (x(to), y(to)) = (xo, 0), for a given x。 * 0 g) find the tangent direction of the solution curves when intersecting the y-axis of two linearly independent functions. h) use the chain rule to show that dx x-5y dy y A-(1¹5) 0 = А 0 along the line x = = = -x + 5y y' = -y dx dy j) make a drawing of the solution curve in the phase plane k) what type of critical point is the origin and determine the stability of this. I) consider the curves given by: and ^ ( )= (-a) A () = ( 5y. How do you interpret this in the phase plane? (C₁+C₂t)e- e-t 5y - and let (x(0), y(0)) = (0,2). Show that x(t) = ½ty and t = − In (52) for 5 > 0. C₂