Solution
= Solution
For column vectors, the second transformation multiplies on the left of the first. Thus the required <matrix> is $SR$, not $RS$. Using the <rotation matrix> convention in part (i),
$$
\boxed{SR=\begin{pmatrix}0&q&q\\1&0&0\\0&-q&q\end{pmatrix},\qquad q=\frac1{\sqrt2}.}
$$
Indeed, a vector first becomes $(x,qy+qz,-qy+qz)$, and the <orthogonal reflection> then exchanges its first two entries.