 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2015/prelims/mathematics-i/3/a/i/solution

Choose the rotation taking

e_{1}

e_{2}

e_{2}

- e_{1}

and

e_{3}

to itself. The columns of the matrix of a linear map are these images of the standard basis, so

A = 010 - 1 00 001 .

This fixes the orientation used throughout this question.

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