Consider the inhomogeneous equation *(t) = [+] A. Calculate the Jordan canonical form J = U-¹ AU of matrix A using MATLA

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Consider The Inhomogeneous Equation T A Calculate The Jordan Canonical Form J U Au Of Matrix A Using Matla 1 (84.56 KiB) Viewed 70 times

Consider the inhomogeneous equation *(t) = [+] A. Calculate the Jordan canonical form J = U-¹ AU of matrix A using MATLAB, including J, U and U−¹. B. Calculate the matrix exponential exp(tA). -7 7 C. Use equation (3.48) to write down the general solution (for arbitrary initial condition x(0) = xo). D. Calculate lim x(t) 0047 xe = x(t) + E. Calculate the constant (equilibrium) solutions e, for which e(t) = 0 (Set the right-hand side equal to zero and solve for (th). For example, you can use undergraduate linear algebra terchniques to solve the system of equations −7x₁ + 7x2 = 1, 7x₁ − 7x2 = −1. Note that there are infinitely many equilibrium points. ). - You don't have to show the following, but it is an interesting fact that while the differential equation is inhomogeneous (with forceing term), the equilibrium solutions œ are stable in the following sense: For all € > 0 there exists > 0 such that if |æ(0) − xe| < d then |x(t) − xe| < € for all t > 0 (that is, solution stays close to xe forever if it starts close to it.)