Consider the following statements with respect to a system represented by its statespace model

\[
\dot{x}=\mathrm{A} x+\mathrm{B} u \text { and } y=\mathrm{C} x
\]

1. The state vector \(x\) of the system is unique.

2. The eigen values of A are the poles of the system transfer function.

3. The minimum number of state variables required is equal to the number of independent energy storage elements in the system.

Which of these statements are correct ?
(a) 1 and 2
(b) 2 and 3
(c) 1 and 3
(d) 1, 2 and 3