Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2010/ia/paper-3/1d/iii/solution

For column vectors, the second transformation multiplies on the left of the first. Thus the required matrix is , not . Using the rotation matrix convention in part (i),
Indeed, a vector first becomes , and the orthogonal reflection then exchanges its first two entries.

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