 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2011/paper-2/14/a/i/solution

Expand the determinant along the first row:

det A = (- 2) (- 12) - 2 (- 6) + (- 3) (- 3) = 24 + 12 + 9.

Thus

det A = 45

. The signs in the middle cofactor account for its positive contribution.

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