Using Maple software, Please help me answer this question (with explanations)

(I don't understand it)

Question 5 Question 5 Insert > > restart: Convert To with (LinearAlgebra) : Execute Format Consider the dynamical system u,, = Au,, _ defined by the matrix A := - 10 ((4, 0, 6) | (0, 8, 0) |(8, 0, 6) ); UI N (5.1) and the initial state vector u0 := (7, 7, 0) : (a) Identify the dominant eigenvalue-eigenvector and classify the origin of this system as attractor, repeller, or saddle point (explain). (b) Find the coordinates (cl, c2, c3) of the initial state vector w0 in the basis of eigenvectors of A. (You can apply 'simplify' command to simplify the final expressions if appropriate) (c) Write the formula for the n-th state u of the dynamical system in terms of a linear combination of eigenvectors of A. Describe the asymptotic (long- term') behaviour of the system on the basis of this formula, in which direction the system will be evolving