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1.1 Find the chawnteristic equation and Hhe eigonanlacs Cand bais for each matrisx. of the corres pun ding eigenspares) of the -3 -4 4 -18 The charar feristic equation ® the eigenvalues (enter your auswer from smallest to langut.) (21, do, ag )= (C a bais for eah He conpeponting igonsparce. X, = D X3 =

6. Complex trigonometric functions, ODE and independence ( 3πT a) Find the real part of following expression: cos +12y-cos 8 8 b) A second order ODE has basis y₁ = cos Ax and y₂ = sin Ax where A is a non-zero constant. i) Identify its eigenvalues and type of damping. ii) Show if these functions are independent with Wronskian. c) A second order ODE has basis y₁ = ³x cos 3x and y₂ = e¯³x sin 3x where B is a constant. i) Identify its eigenvalues and the case of its general solution. ii) Find the ODE.