Let M be a 3 × 3 real matrix such that
\(e^{M \theta}=\left[\begin{array}{ccc} \cos \theta & \sin \theta & 0 \\ -\sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{array}\right] \)
where θ is a real parameter. Then M is given by
1
\(\left[\begin{array}{ccc} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{array}\right]
\)
2
\(\left[\begin{array}{ccc} 0 & 1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 0 \end{array}\right]
\)
3
\(\left[\begin{array}{ccc} 0 & 0 & 1 \\ 0 & -1 & 0 \\ 0 & 0 & 0 \end{array}\right]\)
4
\(\left[\begin{array}{ccc} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{array}\right]
\)