The equation should be:
[ ξ 1 ( t ) ξ 2 ( t ) ] = k 1 e t ( [ 1 0 ] cos 2 t − [ 0 − 1 ] sin 2 t ) + k 2 e t ( [ 1 0 ] sin 2 t + [ 0 − 1 ] cos 2 t ) {\displaystyle {\begin{bmatrix}\xi _{1}(t)\\\xi _{2}(t)\end{bmatrix}}=k_{1}e^{t}\left({\begin{bmatrix}1\\0\end{bmatrix}}\cos 2t-{\begin{bmatrix}0\\-1\end{bmatrix}}\sin 2t\right)+k_{2}e^{t}\left({\begin{bmatrix}1\\0\end{bmatrix}}\sin 2t+{\begin{bmatrix}0\\-1\end{bmatrix}}\cos 2t\right)}
Return to errata.
