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- Find all values of the angle for which the matrix A=[cossinsincos] has real eigenvalues. Interpret your answer geometrically.For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of multiplicity 2. b A has 1 and 2 as eigenvalues. c A has real eigenvalues.P.nilesh
- Let 1 A = -2 1 Consider the system of equations = A. (a) Find all eigenvalues of A. (b) Show that 7 = 0 is the only equilibrium solution of the system. %3D (c) Determine whether 7 Ở is a node, or a saddle, or a spiral point. (d) Determine the stability of 7 = 0. 2.Use a calculator for: - Finding eigenvalues and eigenvectors. - Matrix multiplication still required to show how you find generalized - Matrix inversion - Row reduction - IntegrationPart: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1, 1. -1 -1] A= 1 2 1 -1 Using this diagonalization, write three matrices product in its simplest form for Al0. Is it same for any power Akfor this special matrix A. Part: c: Suppose the rabbit-wolf population (rw) are governed by the following coupled differential equation dr = ar + bw dt dw = cr + dw dt Where a, b, c and d are some unknown constants. If this coupled differential equation is written as a vector differential equation as du = Au dt [a b] where A=" lc dl 1 = |" and u= And given that eigenvalues of A are -3 and -1 with corresponding eigenvectors vi= E&v= find the rabbit and wolf population i.e the functions r(t) and w(t) at any time t if initial rabbit population ro is 2 and wolf population wo is 3?