 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2/17/b/ii/solution

Subtract the first row from the third. Expansion along the resulting row

(a - 1, 0, 0)

det A = (a - 1) det (21 3 a - 1) = (a - 1) (2 a - 5) .

Hence

det A = 0 ⟺ a = 1 or a = \frac{5}{2} .

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