The matrix R(t) is defined by R(t)=costsint−sintcost, then R(s).R(t)=

A
$R (- s - t)$
B
$R (- s + t)$
C
$R (s - t)$
D
$R (s + t)$

Solution:

$\begin{array}{l} R (s) . R (t) = [\begin{array}{l} \cos s & \sin s \\ - \sin s & \cos s \end{array}] [\begin{array}{l} \cos t & \sin t \\ - \sin t & \cos t \end{array}] \\ = [\begin{array}{l} \cos s . \cos t - \sin s . \sin t & \cos s . \sin t + \sin s . \cos t \\ - \sin s \cos t - \sin s \cos t & \cos s . \cos t - \sin s . \sin t \end{array}] \\ = [\begin{array}{l} \cos (s + t) & \sin (s + t) \\ - \sin (s + t) & \cos (s + t) \end{array}] \\ = R (s + t) \end{array}$

The matrix $R (t)$ is defined by $R (t) = [\begin{array}{l} \cos t & \sin t \\ - \sin t & \cos t \end{array}]$ , then $R (s) . R (t) =$

Solution:

Related content