 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-3/1e/ii/solution

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

Integer row and column operations give

(- 4 2 - 6 2) \sim (2 - 4 2 - 6) \sim (20 2 - 2) \sim (2002) .

diag (2, 2) .

The two relation vectors are the columns of the displayed matrix, so its cokernel is the presented module. Consequently

M ≅ Z /2 Z \oplus Z /2 Z .

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