 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ib/paper-1/8e/c/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

The shift matrix obeys

A^{4} = I

and

B = a I + b A + c A^{2} + d A^{3}

. Evaluating

g (t) = a + b t + c t^{2} + d t^{3}

1, i, - 1, - i

gives

a + b + c + d, q u a d a - c + i (b - d), q u a d a - b + c - d, q u a d a - c - i (b - d) .

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