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Consider the matrix A = [a 0 1; 0 b 2; -1 0 c], where a, b, c are positive integers. Given that the trace of A equals 7, find the greatest possible value of the determinant |A|.
- 14
- 15
- 12
- 10
Correct answer: 15
Solution
The determinant expands to abc + b. Testing all positive integer triples summing to 7 shows the maximum value is 15, achieved at (a,b,c) = (2,3,2).
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