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Problem If A 1 , B 1 , C 1 , … A_1, B_1, C_1, \dots A 1 , B 1 , C 1 , … a 1 , b 1 , c 1 , … a_1, b_1, c_1, \dots a 1 , b 1 , c 1 , … Δ = ∣ a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 ∣ , then ∣ B 2 C 2 B 3 C 3 ∣ = \Delta = \begin{vmatrix} a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3 \end{vmatrix}, \text{ then } \begin{vmatrix} B_2 & C_2 \\ B_3 & C_3 \end{vmatrix} = Δ = a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 , then B 2 B 3 C 2 C 3 = a 1 Δ a_1 \Delta a 1 Δ a 1 a 3 Δ a_1 a_3 \Delta a 1 a 3 Δ ( a 1 + b 1 ) Δ (a_1 + b_1) \Delta ( a 1 + b 1 ) Δ Browse the problem library