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

Question

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, 5, 25, 125, 0

MARKS App · Accepted Answer

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

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