1. The state transition matrix for the system $\dot x = Ax$ with initial state x(o) is

- laplace inverse of [(sI – A)
^{-1}x(0)] - laplace inverse of [(sI – A)
^{-1}] - e
^{At}x(0) - (sI – A)
^{-1}

2. The following relation involving state transition matrix φ(t) does not hold true

- φ(t) = I
- φ(t) = φ[(t)]
^{-1} - φ(t
_{1}– t_{2}) = φ(t_{1}– t_{0})φ(t_{2}– t_{0}) - φ(t
_{1}+ t_{2}) = φ(t_{1})φ(t_{2})

3. What is represented by state transition matrix of a system?

- Forced response
- Step response
- Impulse response
- Free response