Problem#11

Given the matrix (attached) Find the rank of A for the different values of r and s

Solve the set of linear equations...

Solve the set of linear equations: a) 4x1 - x2 = 1 x2+ 3x3=0 x1- 4x3=-2 b) 9x2 + x3 - 5x4 = 0 x1+ x2 - 4x4=0 x3 + 8x3=-2 c) 2x1 + 6x3 = 12 3x2+ 2x3=8 5x1 + 3x2 + 3x3=24 8x1 + 6x2 + 14x3=50 For which values of the constant k does the set have no solution? Many solutions? Unique solution?

State Space Representation

Consider the following system (see attachment) whose state space representation is as follows: a) Find the transfer function of the system. b) Compute eAt using the eigenvalues and eigenvectors method. c) Compute eAt using the partial fraction method. d) If u (t)=0 for t ≥ 0,compute x (t), y(t), and x(1) =[ -1 2]T e) Assume that the initial conditions are zero. Using MATLAB ,Plot x(t), y(t), given that u(t)= -5 for 0 ≤ t ≤ 3 and u(t)=5 for 3 ≤ t ≤ 6

Consider the following system whose state space representation is as follows...

Consider the following system whose state space representation is as follows: a) Find the transfer function of the system. b) Compute eAt using the infinite series method. c) Compute eAt using the eigenvalues and eigenvectors method. d) Compute eAt using the partial fraction method. e) Using MATLAB ,Plot x1(t), x2(t), and x3(t),and y(t), when u(t) is a unit step input.

Consider the following system whose state space representation is as follows:

Consider the following system whose state space representation is as follows: a) Assume that the initial conditions are zero. If the reference input is a unit step input , compute x1(t), x2(t), and y(t) b) Find the transfer function of the system. c) Using the transfer function found in (b), Compute y(t). d) Plot x1(t), x2(t), and y(t) using MATLAB