9. An n × n matrix A is called nilpotent if for-one non, negalivew m, we have Ao, If A is a nilpotent matrix prov conider invertible matrix. To prove this tell me what is (1 + AY first the case w...
2. Consider a mass m moving in R3 without friction. It is fasten tightly at one end of a string with length 1 and can swing in any direction. In fact, it moves on a sphere, a subspace of R3 1 0 φ g 2.1 Use the spherical coordinates (1,0,) to derive the Lagrangian L(0,0,0,0) = T-U, namely the difference of kinetic energy T and potential energy U. (Note r = 1 is fixed.) 2.2 Calculate the Euler-Lagrange equations, namely...