 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ia/paper-1/2b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Let

P_{B}, P_{B^{'}}, P_{C}, P_{C^{'}}

have the corresponding basis vectors as columns in standard coordinates. From the PDF,

P_{B} = (02 - 2 0), P_{B^{'}} = (11 1 - 1), P_{C} = 110010001, P_{C^{'}} = I_{3} .

P_{C} A P_{B}^{- 1}

. The change of basis formula therefore gives

A^{'} = P_{C^{'}}^{- 1} P_{C} A P_{B}^{- 1} P_{B^{'}} .

A^{'} = 3/2 5/2 - 1 - 1/2 - 3/2 0 .

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