Consider system \(s_{1}\) modelled as

\[
\begin{aligned}
& \dot{x}=\left[\begin{array}{rr}
2 & 0 \\
0 & -1
\end{array}ight] x+\left[\begin{array}{l}
1 \\
0
\end{array}ight] u \\
& y=\left[\begin{array}{ll}
1 & 0
\end{array}ight] x
\end{aligned}
\]

and system \(s_{2}\) modelled as

\[
\begin{aligned}
& \dot{z}=\left[\begin{array}{ll}
2 & 0 \\
0 & 1
\end{array}ight] z+\left[\begin{array}{l}
1 \\
0
\end{array}ight] u \\
& w=\left[\begin{array}{ll}
1 & 0
\end{array}ight] z
\end{aligned}
\]

What can be predicted about detectability of these systems?
(a) \(s_{1}\) and \(s_{2}\) both are detectable
(b) only \(s_{1}\) is detectable
(c) only \(s_{2}\) is detectable
(d) neither \(s_{1}\) nor \(s_{2}\) is detectable