Consider a system where , and  are three internal state signals and  is the input signal. The differential equations governing the system are given by

Which of the following statements is/are TRUE?

Consider a system S represented in state space as

Which of the state space representations given below has/have the same transfer function as that of S?

The state equation of a second order system is  is the initial condition.

Suppose  and  are two distinct eigenvalues of A and  and  are the corresponding eigenvectors. For constants  and , the solution, , of the state equation is