If a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 = 5 , then the value of b 2 c 3 - b 3 c 2 a 3 c 2 - a 2 c 3 a 2 b 3 - a 3 b 2 b 3 c 1 - b 1 c 3 a 1 c 3 - a 3 c 1 a 3 b 1 - a 1 b 3 b 1 c 2 - b 2 c 1 a 2 c 1 - a 1 c 2 a 1 b 2 - a 2 b 1 is

Step-by-step solution

Let ∆ = a 1 b 1 c 1 a 2 b 2 c 2 a 3 b 3 c 3 = 5 and ∆ ' = b 2 c 3 - b 3 c 2 a 3 c 2 - a 2 c 3 a 2 b 3 - a 3 b 2 b 3 c 1 - b 1 c 3 a 1 c 3 - a 3 c 1 a 3 b 1 - a 1 b 3 b 1 c 2 - b 2 c 1 a 2 c 1 - a 1 c 2 a 1 b 2 - a 2 b 1 here ∆ ' is co-factor determinant of ∆ hence Δ ' = Δ n - 1 ⇒   Δ 3 - 1 =   Δ 2 =   5 2 =   25