The output equation has the output on the left, and the state vector, q(t), and the input u(t) on the right. There are no derivatives on the right hand side. For systems with a single input and single output (i.e., most of the systems we will consider) these variables become (with r=1 and m=1): where. q is n x 1 (n rows by 1 column) A is n x n Let S c R3 be a regular surface and let F: R3 --t R3 be a distance-pre- serving map of R3 (see Exercise 8) such that F(S) c S. Prove that the restric- tion of F to S is an isometry of S. b. Use part a to show that the group of isometries (see Exercise 10) of the unit sphere x2 + y2 + z2 = 1 is contained in the group of orthogonal linear ...

Order my "Ultimate Formula Sheet" https://amzn.to/2ZDeifD Hire me for private lessons https://wyzant.com/tutors/jjthetutorRead "The 7 Habits of Successful ST... So (a;b) is a saddle point of f. If D= 0 (or if rf(a;b) does not exist or fhas more than 2 variables) the test gives no information and you need to do something else to determine if a relative extremum exists.