Answer Happy

Consider the system of differential equations ₁21 +42 =-41 +22 Our goal is first to find the general solution of this system and then a particular solution. In all your answers below, use the scientific calculator notation. For instance 3+5 is written 3 + 51 and 5te a) This system can be written using matrices as X'=AX, where X is in R2 and the matrix A is A ab 6 sin (a) Q a 10 8 Dr b f να b) Find the eigenvalue A of the matrix A with the positive imaginary part and an eigenvector V associated to it. A= ***** a ∞o T R sin (a) n -3t B is written 5'te^(-3).
V = ab sin (a) 8 dx ab f sin (a) 8 c) The general solution of the system of differential equations is of the form 8 f әх a X=c1 X1 + ₂X₂, where c₁ and c₂ are constants, and X₁ and X₂ are the real and imaginary parts of a complex solution. [X1 X₂] = 8 52 α E 52 A E A
[X1 X₂] denotes a matrix with columns X₁ and X₂ respectively. - (2¹)-(3) - d) Find the solution if the initial condition is Answer: X(t) sin (a) 8 Or f ⠀⠀⠀ 8 a att 0. C 12 E 45D Use the scientific calculator notation to define the components 21 (t) and z2 (t). For instance Ste -3t is written 5'te^(-31)