consider the system X(t) = ax(1) + bu(t) with a = 0.001,b= 1,x(0) = 5. (a) Simulate this system using the Matlab command initial (b) Now use u(t) = -kx(t) where k is found as the optimal gain by minimizing the performance index J= ax (1) + ru (1) dt Use q=1, r=1 to simulate this system.
Problem 5. Given the system in state equation form, x=Ax + Bu where (a) A=10-3 01, B=10 0 0-2 (b) A=10-2 01,B=11 Can the system be stabilized by state feedback u-Kx, where K [k, k2 k3l? Problem 5. Given the system in state equation form, x=Ax + Bu where (a) A=10-3 01, B=10 0 0-2 (b) A=10-2 01,B=11 Can the system be stabilized by state feedback u-Kx, where K [k, k2 k3l?
The solution of the IVP dy dx = (ax+by+1)2 – 6; y(0)=0, where a € R and b ERVO} Select one: a. (ax +by+1)(1+x)= 1 O b. (ax+by+1)(1-x)=3 O c. (ax+by+1)2(1 - bx)=1 2 O d. (ax +by+1)= 1- bx e. (ax+by+1)(1-bx)= 1 of. (ax +by+1) (1 -bx)2 = 1 о g. (ax +by-1)(1-bx) = 1 O h. ax + by=1
linear algebra 1 2. Let A be the 3 x 3 matrix: A= 3 3 0 -4 1-3 5 1 (a) Find det(A) by hand. (b) What can you say about the solution(s) to the linear system Az = ? A. No Solutions B. Unique Solution C. Infinitely Many Solutions (c) Is A invertible?
For Exercises 1–21, find dy/dx. Assume a, b, c are constants. x^2 + y^3 = 8 x^2y − 2y +5=0 √x + √y = 25 ax^2 − by^2 = c^2
29&30 please 3 -23 4 3-2 25. 3 4926. |0 1 1 0 0-2 1 2-5 Finding a Basis In Exercises 27-30, find a basis B for the domain of T such that the matrix for T relative to B is diagonal. 27. T: R2→R-T(x, y) = (x + y, x + y) 28. T: R3→R, Tu, y, z) (-2x +2y -3z, 2r y -6z. 2y) a + (af+ 2b)s 29. T: Pi-Pi T(a + bx) 30. T: P㈠Pg Tle...
Please Answer the Following Questions (SHOW ALL WORK) 1. 2. 3. 4. Write an iterated integral for SSSo flexy.z)dV where D is a sphere of radius 3 centered at (0,0,0). Use the order dx dz dy. Choose the correct answer below. 3 3 3 OA. S S f(x,y,z) dx dz dy -3 -3 -3 3 OB. S 19-x2 19-32-22 s f(x,y,z) dy dz dx 19-x2 - 19-2-22 s -3 3 3 3 oc. S S [ f(x,y,z) dy dz dx...
T042 Consider A-2 1 2 0 0 and B -- This overdetermined Ax-B system cannot be solved exactly. The backslash operator gives an approximate 'best' solution. Determine the residual r Ax-B, where x'is the approximation given by the backslash operator. Your answer is the 1-norm of the residual r, rounded to the nearest 0.1 decimal Answer: Check T042 Consider A-2 1 2 0 0 and B -- This overdetermined Ax-B system cannot be solved exactly. The backslash operator gives an...
please provide detailed and clear solutions for the following 2-6 3 2- 0 -103-5 Calculate the determinants of A and B -1 4 (use either appropriate row and coumn expansions or elementary row operations and the properties of determinants). Are A and B invertible? Calculate their inverses if they exist 1b. Are the columns of A linearly dependent or linearly independent? Find the dimension of Nul A and the rank of A. What can you say about the number of...
Problem 5 (a) Let A be an n × m matrix, and suppose that there exists a m × n matrix B such that BA = 1- (i) Let b є Rn be such that the system of equations Ax b has at least one solution. Prove that this solution must be unique. (ii) Must it be the case that the system of equations Ax = b has a solution for every b? Prove or provide a counterexample. (b) Let...