Question

Question B3 (10 marks) Solve the following homogeneous system of first order ODE dai di da dt x,(0)=2. Makesures ou usethe initial with the initial conditions (0):0 0)=1, is in the following form Hint: It is given that one of the solutions of the above system Useful formulas Case 1: A only have distinct roots for λ General solution is ,n) are the coresponding eigenvectors where K, (where i = 1,2, Case 2: For a system of n equations, the coefficient matrix A has a repeated eigenvalue with multiplicities m (that eigenvaule appears m times). Case 2.1: If A is Hermitian, you can find all linearly independent eigenvectors of a with multiplicities m Case 2.2 IfA is not Hermitian, you have to find them by a (m-2) (m-I)1 (A-AI)k- O The Hong Kong Polytechnic Uni A-IKK The general solution is Case 3: A have a pair of complex roots for λ must be K.-B,-iB, If K,-B, +E, is the eiegnvector corresponding to λα, then eiegnvector corresponding to λ The general solution is

Answer 1

3

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