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For a 3x3 determinant D with rows (a1 b1 c1), (a2 b2 c2), (a3 b3 c3), let A1, B1, C1,... be the cofactors of the corresponding elements. Which of the following relations is INCORRECT?

1. a1A1 + b1B1 + c1C1 = D
2. a2A2 + b2B2 + c2C2 = D
3. a3A3 + b3B3 + c3C3 = D
4. a1A2 + b1B2 + c1C2 = D

Correct answer: a1A2 + b1B2 + c1C2 = D

Solution

a1A1+b1B1+c1C1 = D (own row). But a1A2+b1B2+c1C2 = 0 (row 1 elements with row 2 cofactors), so claiming it equals D is incorrect.

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