Please answer all parts and explain when possible Questions

Please answer all parts and explain when possible.

Questions 1 to 5 are regarding the state space representation of a system x = Ax + Bu; y = Cx + Du: System matrix of transfer functions: C(sl - A)^-1B + D can never be 1 times 1. T F The size of the A matrix is only determined by size of x. T F Generally, the number of elements in input vector u, the number of outputs in y and the number of state variables in x vectors may be unrelated. T F C and A matrices must always have the same number of columns. T F C and B matrices must always have the same number of rows. T F Voltage, Force and Pressure are examples of \"Across Variable\" or \"Effort\". T F Current, Volume Flow Rate, and Velocity are examples of \"Through Variable\" or \"Flow\". T F The product of \"flow\" and \"effort\" has units of power for all systems. T F The three linear basic modeling elements: Resistance, Capacitance and Inertia relate their Effort and Flow or their integrals/derivatives by a proportionality constant. T F Example of a liquid system capacitance is a liquid storage tank. T F

Solution

1.F. system matrix of transfer funtion is always 1*1

2.T. size is determined by A

3.F

4.T. C and A must have same number of columns

5.F

6.T

7.T

8.T

9.T

10.T