Consider the system $\dfrac{d x}{d t}=A x+B u$ with $A=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ and $B=\left[\begin{array}{l}p \\ q\end{array}\right]$ where $p$ and $q$ are arbitrary real numbers. Which of the following statements about the controllability of the system is true?
- The system is completely state controllable for any nonzero values of $p$ and $q$
- Only $p=0$ and $q=0$ result in controllability
- The system is uncontrollable for all values of $p$ and $q$
- We cannot conclude about controllability from the given data